Question

Find the area of an isosceles triangle, each of whose equal sides is 18 cm and base is 28
cm. (Take 2 = 1.41)
[Ans. 157.92 cm
​

Answer 1

Concept:-

Here, The all three sides of the isosceles triangle is given, we have to find the area of the isosceles triangle. For finding the area of the isosceles triangle we use Heron's Formula.

Given:-

• Equal sides of the triangle is 18 cm.
• Third side of the triangle is 28 cm.

[Note:- Take √2 = 1.41 ]

To Find:-

• Area of the isosceles triangle ?

Solution:-

Here, We know the Heron's formula for isosceles triangle that is,

$\sf{\Longrightarrow \sqrt{S (S - a)^{2} (S - b)}}$

$\sf{Where,\ S = \dfrac{2a + b}{2}}$

a is the equal side of the triangle

b is the unequal side of the triangle.

We have,

a = 18 cm

b = 28 cm

$\sf{S = \dfrac{2 \times 18 + 28}{2}\ \ \Longrightarrow \ \ 32}$

Now, Putting all the values we get,

$\sf{\Longrightarrow \sqrt{32 (32 - 18)^{2} (32 - 28)}}$

$\sf{\Longrightarrow \sqrt{32 \times (14)^{2} \times 4}$

$\sf{\Longrightarrow \sqrt{32 \times 196 \times 4}$

$\sf{\Longrightarrow \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 7 \times 2 \times 7 \times 2 \times 2 \times 2}$

$\sf{\Longrightarrow \sqrt{\underline{2 \times 2} \times \underline{2 \times 2} \times \underline{2 \times 2} \times \underline{2 \times 2} \times \underline{7 \times 7} \times 2}$

$\sf{\Longrightarrow 2 \times 2 \times 2 \times 2 \times 7 \times \sqrt{2}$

$\sf{\Longrightarrow 112\sqrt{2}$                                  [ Taking √2 = 1.41 ]

$\sf{\Longrightarrow 112 \times 1.41}$

$\sf{\Longrightarrow 157.92\ cm^{2}}$

Hence, Area of the isosceles triangle is 157.92 cm².