Question

A kite in the shape of a square with a diagonal 32cm and an isosceles triangles of base 8cm and sides 6cm 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? [4 MARKS]

Answer 1

Concept : 1 Mark
Application : 1 Mark
Calculations : 2 Marks

We know that
Area of square = $\frac{1}{2}(diagonal{)}^2$

Area of the given kite = $\frac{1}{2}(32cm{)}^2=512c{m}^2$

Area of $1^{st}$ shade = Area of $2^{nd}$ shade
$=\frac{512c{m}^2}{2}=256c{m}^2$

Therefore, the area of paper required in each shape is $256c{m}^2$

For $II{I}^{rd}$ triangle
Semi-perimeter, $s=\frac{(6+6+8)}{2}=10cm$

By Heron’s formula,
Area of triangle = $\sqrt{s(s-a)(s-b)(s-c)}$

Area of IIIrd triangle = $\sqrt{10(10-6)(10-6)(10-8)}=\left(\sqrt{10\times 4\times 4\times 2}\right)c{m}^2=(4\times 2\sqrt{5})c{m}^2=8\sqrt{5}c{m}^2=(8\times 2.24)c{m}^2=17.92c{m}^2$

Area of paper required for IIIrd shade = $17.92c{m}^2$