Question 1 :
State true or false:In $\triangle ABC$, $AB= BC=CA=2a$ and AD is perpendicular to side BC, the area of $\triangle ABC= a^2\sqrt2$.
Question 2 :
The length of each side of an equilateral triangle having an area of $9\sqrt 3 \,\,c{m^2}$ is :
Question 3 :
Find the number of trees that can be planted in a triangular ground having sides $51m, 37m$ and $20m$, when each tree occupies $6m^2$ of space:<br/>
Question 4 :
The sides of a triangle are $5\ cm, 12\ cm$ and $13\ cm$, what is its area?<br/>
Question 5 :
If $G$ is the centroid of the triangle $ABC$, then area of $\Delta AGB=$<br/>
Question 6 :
If the altitude of an equilateral triangle is$\displaystyle \sqrt{6}$ cm its area is
Question 8 :
The altitude drawn to the base of a isosceles triangle is of length $8$ cm and the perimeter is $32$ cm. The area of the triangle is ___________.
Question 9 :
Squares are constructed on the outer side of a right angled triangle on each of its three sides. If the lengths of the two sides containing the right angle are 5 cm and 10 cm respectively, then the total area of the regions bounded by the diagram is
Question 10 :
If the altitude of a triangle is increased by 10% while its area remains the same its corresponding base will have to be decreased by
Question 11 :
If the two legs of a right angled triangle are equal and the square of the hypotenuse is $50$ then the length of each leg is -
Question 12 :
One side of an equilateral triangle is 8 cm. Its area is
Question 13 :
Each of the base angle of an isosceles triangle is twice the vertical angle then the vertical angle is
Question 14 :
Find the area of equilateral triangle with side $ 4\sqrt { 3 }\ cm$
Question 15 :
The sides of a $\Delta$ are $7 cm, 24 cm$ and $25 cm$. Find its area.
Question 16 :
If two sides of an isosceles triangle are 6 cm and 11 cm then the length of the third side is -
Question 17 :
If s is the semi-perimeter of a $\Delta A B C$ whose sides are a,b,c then s=.............?<br><br>
Question 18 :
In $\triangle ABC, AB = 6\ cm, BC = 7\ cm$ and $AC = 5\ cm$. Find the area of $\triangle ABC$
Question 19 :
One side of an equilateral triangle is 30 cm Its area is
Question 20 :
Find the area of an equilateral triangle whose each measures $8\ cm$.
Question 21 :
Find the area of a triangle whose sides are respectively $150$ cm, $120$ cm and $200$ cm. 
Question 22 :
The sides of a triangle are 5 cm, 12 cm and 13 cm. Then its area is<br>
Question 23 :
An isosceles right triangle has area $112.5$ sq. cm. The length of its hypotenuse (in cm) is
Question 24 :
If the side of an equilateral triangle is decreased by $20\%$, its area is decreased by
Question 25 :
One side of an equilateral triangle is 30 cm Its area is
Question 26 :
In a triangular field having sides 30 m, 72 m and 78 m , the length of the altitude to the side measuring 72 m is
Question 27 :
If the altitude of an equilateral triangleis $\sqrt 6$ cm, its area is
Question 28 :
A square and an equilateral triangle have equalperimeters. If the diagonal of the square is $6\sqrt 2 cm$, then the area of the triangle is
Question 29 :
Area of an equilateral triangle of side 'a' units can be calculated by using the formula :
Question 30 :
Within an equilateral triangle of side $6$ cm two other equilateral triangles having the same centroid are so drawn that they divide the triangle into three parts having equal areas. The side of one of the triangle is
Question 31 :
Area of traingle ABC whose sides are 24m, 40m and 32m is-
Question 32 :
A parallelopiped is formed by planes drawn through the points $(2,3,5)$ and $(5,9,7),$ parallel to the coordinate planes. The length of a diagonal of the parallelopiped is 
Question 33 :
The area of a triangle whose sides are $4\ cm, 13\ cm$ and $15\ cm$, is<br/>
Question 34 :
The sides of an equilateral triangle are (2a - b)cm, (a + 3b) cm and (2a - 2b + 1) cm then the perimeter of the triangle is
Question 35 :
The lenghts of the sides of a triangle are 9 cm 12 cm and 15 cm then the length of the median to the longest side is
Question 36 :
If A is the area of a triangle in$ \displaystyle cm^{2}m $ whose sides are 9 cm, 10 cm, and 11 cm then which one of the following is correct ?
Question 37 :
Two sides of a right triangle containing the right angle are 100 cm and 4.6 cm. Find its area---
Question 38 :
The perimeter of a triangular field is 144 m and the ratio of the sides is 3 : 4 : 5 The area of the field is
Question 39 :
The side of an equilateral triangle of area $64\sqrt { 3 } { cm }^{ 2 }$ is
Question 41 :
Two sides of a right triangle containing the right angle are $100 cm$ and $8.6 cm$. Find its area
Question 42 :
The three sides of a triangle are $3cm,4cm$ and $5cm$ respectively; then its area is:
Question 43 :
If the vertices of a triangle are (2,4), (5,k) and (3,10) and its area is 15 sq. units, the value of k is
Question 44 :
Area of an equilateral triangle of side $a$ units can be calculated by using the formula :<br/>
Question 45 :
The sides of a triangle are 3 cm, 4 cm and 5 cm. Its area is<br>
Question 47 :
If every side of a triangle is doubled, then the area of the new triangle is 'K' times the area of the old one. The value of K is<br>
Question 48 :
The sides of a triangle are $3$ cm, $5$ cm and $4$ cm: Its area is
Question 49 :
The sides of a triangle are $4, 5$ and $6$ cm. The area of the triangle is equal to
Question 50 :
The angle between the external bisectors of two angles of a triangle is$\displaystyle 50^{\circ}$ then the third angle is
Question 51 :
Find the area of a triangle with sides having length $40, 24$ and $32 m$
Question 52 :
The area of a square is equal to the area of a circle. What is the ratio between the side of the square and the radius of the circle ?
Question 54 :
In a quadrilateral ABCD if $AB=CD,\quad AB\parallel CD\quad and\quad AB=BC$, then ABCD is a
Question 55 :
A land ABCD is in the shape of a Quadrilateral has $\angle C = 90, AB = 9m, BC = 12m, CD = 5m$ and $AD = 8m$. How much area does it occupy?
Question 56 :
In parallelogram ABCD, AB $=$ (x+8) cm and CD $=$ (3x-2) Then AB equals
Question 57 :
Use Heron's formula to find the area of a triangle of lengths $4, 5$ and $6.$
Question 58 :
$\angle A\quad and\quad \angle C$ of a quadrilateral ABCD are ${ 65 }^{ }$ each and the other two are equal angles. Then the quadrilateral is a
Question 59 :
A triangle and a parallelogram have the same base and the same area. If the side of the triangle are 13 cm, 14 cm, and 15 cm and the parallelogram stands on the base 14 cm, find the height of the parallelogram.
Question 60 :
If the sides of a triangle are doubled, then its area <br/>
Question 61 :
Find the area of a triangle, two of its sides are $8 cm$ and $11 cm$ and the perimeter is $32 cm$.
Question 62 :
If PQRS is a parallelogram with PR $=$ QS, then PQRS is a
Question 63 :
The diagonal of a square A is $(x+y)$. The diagonalof square B with twice the area of A is
Question 64 :
The opposite sides of a parallelogram are represented by $3x + 12$ and  $5x - 20$. Find the length of the side of the parallelogram represented by $2x - 5$.<br/>
Question 65 :
The angles of a quadrilateral are in the ratio $3:5:9:13$. All the angles of the quadrilateral are
Question 67 :
Use Heron's formula to find the area of a triangle of lengths $5 cm, 9 cm$ and $12 cm$.
Question 68 :
The side of a rhombus is $10$ cm and one diagonal is $16$ cm. The area of the rhombus is<br/>
Question 69 :
For a quadrilateral, with the $4$ sides given and with none of the angles $90^o,$ <br/>
Question 70 :
What is the volume (in $\displaystyle cm^{3}$) of the prism whose base is a hexagon of side 6 cm and height$\displaystyle 12\sqrt{3}$ cm?
Question 71 :
The area of a rectangular garden is $2100$ $ft^2$. Find the width if its height measures $20$ ft.<br/>
Question 72 :
The sides of a triangle are $5y, 6y $ and $9y$. find an expression for its area $A$.
Question 73 :
A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are $15 cm, 14 cm, 13 cm$, and the parallelogram stands on the base of $15$ cm. Find the height of the parallelogram.
Question 74 :
Use Heron's formula to find the area of a triangle of lengths $7, 8$ and $9$.
Question 76 :
Find the area of a rhombus with sides 20 cm and length of one of the diagonal as 28 cm.
Question 77 :
A kite with $x$ cm, $x$ cm, $y$ cm and $y$ cm is inscribed in a circle. The area of the kite is
Question 78 :
The area of an isosceles triangle having base 2 cm and the length of one of the equal sides 4 cm, is<br>
Question 79 :
The dimensions of a car petrol tank are $\displaystyle 50cm\times 32cm\times 24cm,$ which is full of petrol. If car's average consumption is 15 km per litre, find the maximum distance that can be covered by the car.<br>
Question 81 :
A wire of length $50\: cm$ is to be bent in the form of a parallelogram of area $50\: cm^{2}$. If the angle between the adjacent sides is $30^{\circ}$, then the dimensions of the parallelogram are<br/>
Question 82 :
A piece of wire 132 dm long is bent successively in the shape of an equilateral triangle a square a regular hexagon and a circle Then the area included is largest when the shape is
Question 83 :
The parallel sides of a parallelogram are $20$ and $10$ m and one of the diagonals is $12$ m. Find the area of the parallelogram. (Use Heron's formula)<br/>
Question 84 :
The sides of a triangular plot are in the ratio of $3:5:7$ and its perimeter is $300m$. Find its area.
Question 85 :
The adjacent sides of a parallelogram are 8 cm and 9 cm. The shorter diagonal is 13 cm. What is its area?
Question 86 :
A rectangular cupboard is of length 3 m and perimeter 30 m. Find the width of the cupboard.<br>
Question 87 :
Find the area of the parallelogram with sides $10 cm$ and $12 cm$ and one of the diagonals as $14 cm.  $
Question 88 :
If the angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4, then the smallest angle in the centesimal system is _____
Question 89 :
The area of a square plot of land is 7056$m^{2}$. Find the expenditure for five layered wiring around the plot at Rs 8 per meter.
Question 90 :
The lengths of sides of a triangle are in the ratio $3:4:5$ and its perimeter is $144$ cm, then find the height corresponding to largest side.
Question 91 :
The parallel sides of a parallelogram are $40$ and $15$ m and one of the diagonals is $35$ m. Find the area of the parallelogram, if the distance between the parallel sides is $50$ m. (Use Heron's formula)<br/>
Question 92 :
If PQRS is a parallelogram with PR $=$ QS, and PR is perpendicular to QS,then PQRS is a
Question 93 :
What is the area of a rhombus whose diagonals are of lengths 4 cm and 2.5 cm?<br>
Question 94 :
Surya has a land in the shape of a rhombus. He wants to cultivate rice and wheat. he divided the land in two equal parts. The perimeter of the land is $400 m$ and one of the diagonals is $160m$, how much area is available for rice ?
Question 95 :
The lengths of the sides of a  triangle are in integers and its area is also an integer. One side is $21$ cm and the  perimeter is $48$ cm, then the length of the shortest side is <br/>
Question 96 :
The sides of a triangle are 35cm, 54cm and 61cm, respectively. The length of its longest altitude is<br/>
Question 97 :
The diagonals of a rhombus are $16$ and $30$. Find the perimeter of the rhombus.<br/>
Question 98 :
Find the area of a triangle with two equal sides of $5 cm$ and remaining one of $8 cm$.
Question 99 :
In aparallelogram, PQRS, $PR\neq QS\quad and\quad PR\pm QS$. Then PQRS is a
Question 100 :
<font color="#4d4d4d" face="Alegreya">A quadrilateral $ABCD$ has $\angle C =90,AB=9 cm,BC=8cm,CD=6cm$ and $AD=7 cm.$ How much area does it occupy?</font><br/>
Question 101 :
If an angle of a triangle remains unchanged but each of its two including sides is doubled, then the area is multiplied by:
Question 102 :
Using Heron's formula find the area of a quadrilateral whose sides are $3\ cm, 4\ cm, 4\ cm$, and $5\ cm$. The angle between the first two sides is $90^0$. <br/>
Question 103 :
The triangular side - wall of a flyover have been used for advertisements, The sides of the walls are 122 m, 22m and 120 m. The advertisements requires rent of Rs 5000 per $\displaystyle m^{2}$ per year. A company hired one of its walls for 3 months. How much rent did it pay ?
Question 104 :
Find the area of a quadrilateral whose sides are $3\ cm, 4\ cm, 2\ cm$, and $5\ cm$. The angle between the first two sides is $90^o$. (Use Heron's formula)<br/>
Question 105 :
If the height of an equilateral triangle is $9$, what is its area?
Question 106 :
The vertices of a triangle are (2, 0), (-2, -1), and (3, -4). The triangle is
Question 107 :
The vertices of a triangle are the intersections of the lines whose equations are y = 0, x = 3y, and 3x + y = 7. This triangle is
Question 108 :
The sides of a triangle are 11 cm 15 cm and 16 cm The altitude to largest side is
Question 109 :
If A, B, C, D are angles of a cyclic quadrilateral , find the value of $cos A + cos B + cos C + cos D$.
Question 110 :
An equilateral triangle and a regular hexagon have the same perimeter. If the area of the hexagon is $72\sqrt{3}$, calculate the area of the triangle.
Question 111 :
The difference between the area of a square and that of an equilateral triangle on the same base is $\displaystyle \frac{1}{4}cm^{2}$. What is the length of the side of the triangle?
Question 112 : <p>A traffic signal board, indicating 'SCHOOLAHEAD', is an equilateral triangle with side $a$. Find the area of the signal board, using Heron's formula. If its perimeter is $180 cm$, what will be the area of the signal board?</p>
Question 113 :
$ABCD$ is a parallelogram $AB=14\;cm,BC=18\;cm,AC=16\;cm$ then the length of the length of the other diagonal.
