Area of a Triangle

Q. Find the area of right angled triangle whose hypotenuse is 15 cm and one of the sides is 12 cm.

1. $45c{m}^2$
2. $54c{m}^2$
3. $35c{m}^2$
4. $27c{m}^2$

Q. The perimeter of a square and an equilateral triangle are equal. If the length of side of equilateral triangle is 4 cm more than that of the square, then find the perimeter of the square.

1. 16 cm
2. 48 cm
3. 36 cm
4. 12 cm

Q.

Find the area of triangle whose base is 4 cm and height of triangle is 12 cm.

1. $24c{m}^2$

2. $12c{m}^2$

3. $18c{m}^2$

4. $\text{None of these}$

Q. For the same perimeter, has the largest area.

1. a square
2. a rectangle
3. a circle

Q. If the area of a triangle is $54c{m}^2$ and its height is three times its base, then find the base.

1. $6cm$
2. $7cm$
3. $6.5cm$
4. $7.5cm$

Q. Figures having the same perimeter must have the same area as well.

1. False
2. True

Q.

Find the area of the following shape (in sq. cm) [4 MARKS]

Q. The base of an isosceles triangle is $\frac{4}{3}$. The perimeter of the triangle is $4\frac{2}{15}$ cm.

Q. Which of the following combination of base and height is not possible if the area of the triangle is given as $36c{m}^2$?

1. $12cm,6cm$
2. $9cm,8cm$
3. $24cm,3cm$
4. $9cm,4cm$

Q. The ratio of the base and height of a triangle is 4 : 5. If the area of the triangle is 1440 $m^2$, find the measurement of its base and height.

1. 42 m, 60 m
2. 48 m, 62 m
3. 48 m, 60 m
4. 46 m, 68 m

Q. 1.If the lengths of the sides of a triangle are in the ratio $3:4:5$ and its perimeter is $48cm$. Find its area.
2.The sides of a triangular plot are in the ratio $3:5:7$ and its perimeter is $300m$. Find its area (Take $\sqrt{3}=1.732$)

Q. The perimeter of an equilateral triangle is 24.9 cm. Find its side.

1. 12.45 cm
2. 6.25 cm
3. 8.3 cm
4. 9.1 cm

Q. Find the area of an isosceles triangle whose equal sides are $5cm$ and base is $8cm$.

Q.

Find the area of the figure given below (in sq. inches).

1. 84
2. 96
3. 48
4. 64

Q. How to derive general formula in algebra
$Ex=2,5,10,17,26,37,50,65,82,101,$ ?

Q.

A local park is 32 m long and its width is half of the length. It has two right-triangular grass lawns with the following dimensions. The local gardener wanted to renovate the park so he hired some men. The men agreed to work on the grass lawn at Rs. 1.2 per sq metre and put new footpath at Rs. 0.80 per sq metre. What is the total cost the gardener will have to pay after the work is done?

1. ₹​ 431.2

2. ₹​ 368.4

3. ₹​ 421.8

4. ₹​ 512

Q.

Find the area of figure given below (in sq. inches).

1. 48
2. 64
3. 84
4. 96

Q.

Find the area of the figure given below (in sq. inches). [4 MARKS]

Q. In the figure given below, identify the right angled triangle.

1. ΔBAC
2. ΔAMB
3. ΔANC
4. ΔAMN

Q.

If the area of a triangle is $49c{m}^2$ and its base is double its height, then find the height.

1. 6 cm

2. 9 cm

3. 24 cm

4. 7 cm

Q. A local park is 32 m long and its width is half of the length. It has two right-triangular grass lawns with the following dimensions. The local gardener wanted to renovate the park so he hired some men. The men agreed to work on the grass lawn at ₹​ 1.2 per sq metre and put new footpath at ₹ 0.80 per sq metre. What is the total cost the gardener will have to pay after the work is done?

1. ₹​ 431.2
2. ₹​ 368.4
3. ₹​ 421.8
4. ₹​ 512

Q.

Find the area of the following shape (in sq. cm) [4 MARKS]

Q. The base of triangle $T$ is $40$ percent less than the length of rectangle $R$. The height of triangle $T$ is $50$ percent greater than the width of rectangle $R$. The ratio of the area of triangle $T$ to that of the area of rectangle $R$ converted to $\%$ is :

1. $10$
2. $45$
3. $90$
4. $110$

Q.

A room is 4 m long and 3 m 50 cm wide. How many square metres of carpet is needed to cover the floor of the room?

Q. For what value of $x$ are the points $(1,3),(2,2)$ and $(x,3)$ collinear?

Q.

The base of a triangular field is 2.4 times its height. If the cost of levelling the field at the rate of ₹20 per square meter is ₹9600, then the height of the field is ___ m.

1. 20

2. 30

3. 48

4. 50

Q. Find the area in square metre of a piece of cloth 1m 25 cm wide and 2 m long.
[2 marks]

Q. Which of the following sets of side lengths will not form a triangle?

1. $11$ cm, $10$ cm, $11$ cm
2. $3$ m, $3$ m , $3$ m
3. $3$ cm, $4$ cm, $7$ cm
4. $9$ mm, $9$ mm, $12$ mm

Q. Area of quadrilateral ABCD is 20 ${cm}^2$ and perpendiculars on BD from opposite vertices are 1 cm and 1.5 cm. The length of BD is _______.

Q.

An isosceles triangle has perimeter 36 cm. If each of the equal sides is 10 cm, then the area of the triangle is _____${\text{cm}}^2$

1. 48

2. 38

3. 44

4. 45