Question 1 :
If each side of a triangle is doubled, then find the ratio of area of the new triangle thus formed and the given triangle.

Question 2 :
The sides of a triangular plot are in the ratio of 3 : 5 : 7 and its perimeter is 300 m. Find its area

Question 3 :
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 4 :
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 5 :
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 6 :
<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 7 :
The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 13 m, 14 m and 15 m. The advertisements yield an earning of Rs 2000 per $m^2$ a year. A company hired one of its walls for 6 months. How much rent did it pay?

Question 8 :
The sides of a triangle are 35 cm, 54 cm and 61 cm, respectively. Find the length of its longest altitude.

Question 9 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1bff59b460d7261f4bb.JPG' /> Refer to the above image. The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122 m, 22 m and 120 m. The advertisements yield an earning of $Rs. 5000/m^2$ per year. A company hired one of its walls for 3 months. How much rent did it pay?

Question 10 :
<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 11 :
Find the area of an isosceles triangle having base 2 cm and the length of one of the equal sides 4 cm.

Question 12 :
<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 13 :
An isosceles right triangle has area 8 $cm^2$. The length of its hypotenuse is

Question 16 :
Write True or False. If the side of a rhombus is 10 cm and one diagonal is 16 cm, the area of the rhombus is 96 $cm^2$.

Question 17 :
<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 18 :
<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 19 :
<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 21 :
Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540cm. Find its area.

Question 22 :
Find the length of each side of an equilateral triangle having an area of $9\sqrt{3}$ $cm^2$.

Question 24 :
The sides of a quadrilateral ABCD are 6 cm, 8 cm, 12 cm and 14 cm (taken in order) respectively, and the angle between the first two sides is a right angle. Find its area.

Question 25 :
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 26 :
The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.

Question 28 :
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. find the cost of fencing it with barbed wire at the rate of Rs 20 per metre leaving a space 3m wide for a gate on one side.

Question 29 :
Find the area of a triangle, two sides of which are 8 cm and 11 cm and the perimeter is 32 cm.

Question 30 :
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.