Area of an Isosceles Triangle

Q.

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.

Q.

The semi perimeter of a triangle is 132cm. The product of the difference of semi perimeter and it's respective side is 13200cm³. Find the area of triangle.

Q.

$\text{The base of an isosceles triangle is 16 cm and its area is 48}c{m}^2.\text{The perimeter of the triangle is}\left(a\right)41cm\left(b\right)36cm\left(c\right)48cm\left(d\right)324cm$

Q.

Find the area of an isosceles triangle each of whose equal sides measures 13 cm and whose base measures 20 cm.

Q. If an isosceles triangle has a perimeter of $20cm$ and base $4cm$, then its area is ___ .

1. $2\sqrt{15}c{m}^2$
2. $4\sqrt{15}c{m}^2$
3. $2\sqrt{15}c{m}^2$
4. $4\sqrt{3}c{m}^2$

Q. Find the area of the shaded region in the figure given below.

1. 576 cm${}^2$
2. 96 cm${}^2$
3. 480 cm${}^2$
4. 384 cm${}^2$

Q. Is the following formula to calculate the area of an isoscles triangle true or false?
$\frac{b}{4}\times \sqrt{4a^2-b^2}$ , where b is the base and a is the length of the equal sides.

1. True
2. False

Q. Question 8
The area of an isosceles triangle having base 2cm and the length of one of the equal sides 4cm, is

Q. If each side of a equilateral triangle is tripled then what is the percentage increase in the area of the triangle?

Q.

Find the area of the triangle with sides, 56 cm, 52 cm, 60 cm.

Q.

The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122m, 22m, and 120m (see the given figure). The advertisements yield an earning of Rs 5000 per m² per year. A company hired one of its walls for 3 months. How much rent did it pay?

Q.

The formula to find the area of a triangle: $\frac{1}{2}\times$base$\times$height, is valid only for a right angled triangle.

1. False

2. True

Q. The area of an isosceles triangle having equal side 5 cm is 12 cm${}^2$. The third side of the triangle is

1. 8 cm
2. 4 cm
3. 7 cm
4. 10 cm

Q. PQRS is a trapezium such that PQ || RS and PQ = 10 cm, QR = 5 cm, RS = 8 cm and PS = 5 cm, then area of PQRS is

1. 
   $12\sqrt{3}c{m}^2$
2. 
   $18\sqrt{6}c{m}^2$
3. 
   $24\sqrt{3}c{m}^2$
4. 
   $12\sqrt{6}c{m}^2$

Q.

If the base and height of triangular wall is 4m and 6m respectively, Then the area of the triangle is 12$m^2$.

1. True

2. False

Q. The area of an isosceles triangle is $48c{m}^2$. If the length of the altitude to the non-equal side is 8 cm, then the length of the equal sides of the triangle is

1. 12 cm
2. 6 cm
3. 10 cm
4. 8 cm

Q. The perimeter of a right triangle is 144cm and it's hypotenuse measure 65 cm . Find the length of other two sides and calculate it's area verify the results using Herons formula

Q.

How much Percentage of area of an equilateral triangle will increase if it's side is increased 3 times?

Q. The area of an isosceles triangle with sides $17cm,17cmand30cm$ is

1. 
   $289c{m}^2$
2. 
   $240c{m}^2$
3. 
   $60c{m}^2$
4. 
   $120c{m}^2$

Q. How to find the area of isosceles triangle ?

Q.

There is a slide in the park. One of its side walls has been painted in the same colour with a message “KEEP THE PARK GREEN AND CLEAN” (see the given figure). If the sides of the wall are 15m, 11m, and 6m, find the area painted in colour.

Q. The perimeter of an isosceles triangle is 42 cm and its base is (3/2) times each of the equal sides. Find the length of each side of the triangle, area of the triangle and the height of the triangle.

Q.

A traffic signal board including SCHOOL AHEAD is an equilateral triangle with side 'a'. Find the area of the signal board using heron's formula if its perimeter is 180cm. What will be the area of the signal board?

Q.

Assertion : The sides of a triangle are $3\mathrm{cm},4\mathrm{cm}$ and $5cm$ . Its area is $6{\mathrm{cm}}^2$.

Reason : If $2s=(a+b+c)$, where $a,b,c$ are the sides of a triangle, then area $=\sqrt{(s-a)(s-b)(s-c)}$

Which of the following is correct?

1. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

2. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.

3. If Assertion is correct but Reason is incorrect.

4. If Assertion is incorrect but Reason is correct.

Q.

A kite in the shape of a square with a diagonal 32 cm and an isosceles triangles of base 8 cm and sides 6 cm each is to be made of three different shades as shown in the given figure. How much paper of each shade has been used in it?

Q. Is the following formula to calculate the area of an isoscles triangle true or false?
$\frac{b}{4}\times \sqrt{4a^2-b^2}$ , where b is the base and a is the length of the equal sides.

1. True
2. False

Q.

The perimeter of an isosceles triangle is 32cm.The ratio of equal side to its base is 5:4.Find the area?

Q. The area of the triangle whose two sides are 18cm and 10cm, respectively and the perimeter equal to 42 cm is $21\sqrt{11}$Sq cm.

1. True
2. False

Q.

By Hero's formula the area of triangle is $\sqrt{s(s-a)(s-b)(s-c)}$

1. True

2. False

Q. Find the area of the shaded region in figure: