Question 1 :
If the area of an equilateral triangle is $16\sqrt{3}$ $cm^2$, then find the perimeter of the triangle.

Question 2 :
Write True or False. The area of the isosceles triangle is $\frac{5}{4}\sqrt{11}cm^2$, if the perimeter is 11 cm and the base is 5 cm.

Question 3 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1bdf59b460d7261f4b9.JPG' /> Refer to the above image. Sanya has a piece of land which is in the shape of a rhombus. She wants her one daughter and one son to work on the land and produce different crops. She divided the land in two equal parts. If the perimeter of the land is 400 m and one of the diagonals is 160 m, how much area each of them will get for their crops?

Question 4 :
An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.

Question 5 :
The edges of a triangular board are 6 cm, 8 cm and 10 cm. Find the cost of painting it at the rate of 9 paise per $cm^2$.

Question 7 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d134f59b460d7261f3f4.JPG' /> From the above image, how much paper of yellow shade is needed to make a kite in which ABCD is a square with diagonal 44 cm?

Question 8 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d133f59b460d7261f3f3.JPG' /> From the above image, ∆ ABC has sides AB = 7.5 cm, AC = 6.5 cm and BC = 7 cm. On base BC a parallelogram DBCE of same area as that of ∆ ABC is constructed. Find the height DF of the parallelogram.

Question 10 :
The perimeter of a triangular field is 420 m and its sides are in the ratio 6 : 7 : 8. Find the area of the triangular field.

Question 11 :
A rectangular plot is given for constructing a house, having a measurement of 40 m long and 15 m in the front. According to the laws, a minimum of 3 m, wide space should be left in the front and back each and 2 m wide space on each of other sides. Find the largest area where house can be constructed.

Question 12 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d137f59b460d7261f3f9.JPG' /> From the above image, a design is made on a rectangular tile of dimensions 50 cm × 70 cm. The design shows 8 triangles, each of sides 26 cm, 17 cm and 25 cm. Find the remaining area of the tile.

Question 13 :
Write True or False. The area of a regular hexagon of side $a$ is the sum of the areas of the five equilateral triangles with side $a$.

Question 14 :
An Isosceles triangle, with base a and equal sides b, what will be it's area formula?

Question 15 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1bcf59b460d7261f4b7.JPG' /> Refer to the above image. Students of a school staged a rally for cleanliness campaign. They walked through the lanes in two groups. One group walked through the lanes AB, BC and CA; while the other through AC, CD and DA. Then they cleaned the area enclosed within their lanes. If AB = 9 m, BC = 40 m, CD = 15 m, DA = 28 m and $\angle B = 90^{\circ}$, Find the total area cleaned by the students.

Question 17 :
Write True or False. In a triangle, the sides are given as 11 cm, 12 cm and 13 cm. The length of the altitude is 10.25 cm corresponding to the side having length 12 cm.

Question 18 :
Write True or False. The area of ∆ ABC is 8 $cm^2$ in which AB = AC = 4 cm and $∠A = 90^\circ$.

Question 19 :
From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 14 cm, 10 cm and 6 cm. Find the area of the triangle.

Question 20 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d137f59b460d7261f3f8.JPG' /> From the above image, the dimensions of a rectangle ABCD are 51 cm × 25 cm. A trapezium PQCD with its parallel sides QC and PD in the ratio 9 : 8, is cut off from the rectangle. If the area of the trapezium PQCD is $\frac{5}{6}th$ part of the area of the rectangle, find the lengths PD.

Question 21 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1baf59b460d7261f4b4.JPG' /> Refer to the above image. Kamla has a triangular field with sides 240 m, 200 m, 360 m, where she grew wheat. In another triangular field with sides 240 m, 320 m, 400 m adjacent to the previous field, she wanted to grow potatoes and onions. She divided the field in two parts by joining the mid-point of the longest side to the opposite vertex and grew potatoes in one part and onions in the other part. How much area is been used for wheat ? $\begin{pmatrix}1\ hectare = 10000 m^2\end{pmatrix}$

Question 22 :
A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm, is painted on both sides at the rate of Rs 5 per $m^2$ . Find the cost of painting.

Question 23 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1c2f59b460d7261f4bf.PNG' /> Refer to the above image. A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in above figure. How much paper of shade has been used in 1 and 2 part it?

Question 25 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d133f59b460d7261f3f2.JPG' /> From the above image, find the area of the trapezium PQRS.

Question 26 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d135f59b460d7261f3f5.JPG' /> From the above image, how much paper of red shade is needed to make a kite in which ABCD is a square with diagonal 44 cm?

Question 27 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1bdf59b460d7261f4b8.JPG' /> Refer to the above image. Kamla has a triangular field with sides 240 m, 200 m, 360 m, where she grew wheat. In another triangular field with sides 240 m, 320 m, 400 m adjacent to the previous field, she wanted to grow potatoes and onions. She divided the field in two parts by joining the mid-point of the longest side to the opposite vertex and grew potatoes in one part and onions in the other part. How much area is been used for onions ? $\begin{pmatrix}1\ hectare = 10000 m^2\end{pmatrix}$

Question 29 :
Find the cost of laying grass in a triangular field of sides 50 m, 65 m and 65 m at the rate of Rs 7 per $m^2$.

Question 30 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1c0f59b460d7261f4bd.PNG' /> Refer to the above image. A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in above figure. How much paper of shade has been used in 3 part?

Question 31 :
A triangular park ABC has sides 120m, 80m and 50m. A gardener Dhania has to put a fence all around it and also plant grass inside. How much area does she need to plant?

Question 32 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1bef59b460d7261f4ba.JPG' /> There is a slide in a park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN”. If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.

Question 33 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1c1f59b460d7261f4be.PNG' /> Refer to the above image. A floral design on a floor is made up of 16 tiles which are triangular, the sides of the triangle being 9 cm, 28 cm and 35 cm. Find the cost of polishing the tiles at the rate of 50 paise per $cm^2$ .

Question 34 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d139f59b460d7261f3fb.png' /> From the above figure, calculate the area of the shaded region.

Question 35 :
If a, b, c are the lengths of three sides of a triangle, then area of a triangle =$\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$, where s = perimeter of triangle. Write True or False.

Question 36 :
Write True or False. The cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of Rs 3 per $m^2$ is Rs 918.

Question 38 :
Write True or False. The base and the corresponding altitude of a parallelogram are 10 cm and 3.5 cm, respectively. The area of the parallelogram is 30 $cm^2$.

Question 39 :
The sides of a triangular plot are in the ratio of 3 : 5 : 7 and its perimeter is 300 m. Find its area

Question 40 :
The sides of a triangular field are 41 m, 40 m and 9 m. Find the number of rose beds that can be prepared in the field, if each rose bed, on an average needs 900 $cm^2$ space.

Question 41 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d132f59b460d7261f3f1.JPG' /> From the above image, find the length of the altitude from vertex A on the side DC.

Question 42 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d131f59b460d7261f3f0.JPG' /> From the above image, find the area of a parallelogram.

Question 43 :
The base of a right triangle is 8 cm and hypotenuse is 10 cm. Find its area.

Question 44 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d136f59b460d7261f3f7.JPG' /> From the above image, the dimensions of a rectangle ABCD are 51 cm × 25 cm. A trapezium PQCD with its parallel sides QC and PD in the ratio 9 : 8, is cut off from the rectangle. If the area of the trapezium PQCD is $\frac{5}{6}th$ part of the area of the rectangle, find the lengths QC.

Question 45 :
Find the length of each side of an equilateral triangle having an area of $9\sqrt{3}$ $cm^2$.