Name: Area of a Triangle by Heron's Formula
Uploaded: 2019-07-19
Duration: 7 min 5 s
Description: Do you know how to calculate the area of a triangle when all three side lengths are given? It is very easy. Watch this video to understand how to calculate.

Question

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

Accepted Answer

We need to find the areas of $I, II$ and $III$ .

Areas $I$ and $II$ forms a square.

We know that,

Area of square $= \frac{1}{2} \times {(d i a g o n a l)}^{2}$
$= \frac{1}{2} \times {(32)}^{2}$

$= 512 {cm}^{2}$

So, the area of part $I$ shade $=$ the area of part $II$ shade

$= \frac{512}{2} {cm}^{2} = 256 c m^{2}$

For part $III$ , which is a triangle,

Semi perimeter, $s = \frac{(6 + 6 + 8)}{2} = 10 c m$

According to Heron's formula,

Area of a triangle $= \sqrt{s (s - a) (s - b) (s - c)}$ , where

$a, b, c$ are the sides of the triangle.

So, substituting the given values,

$= \sqrt{10 (10 - 6) (10 - 6) (10 - 8)}$

$= \sqrt{10 \times 4 \times 4 \times 2} c m^{2}$

$= 4 \times 2 \sqrt{5} c m^{2}$

$= 8 \sqrt{5} c m^{2}$

$= 8 \times 2.24 c m^{2}$

$= 17.92 c m^{2}$

Hence, area of the paper required for $I$ and $II$ shade is $256 {cm}^{2}$ and for $III$ shade, the area is $17.92 c m^{2}$ .

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

Important Questions on Heron's Formula

Learn and Prepare for any exam you want !

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 the figure. How much paper of each shade has been used in it?

Important Questions on Heron's Formula

Learn and Prepare for any exam you want !

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