Question 7
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?
We know that
Area of Kite = 12(diagonal)2
Area of the given kite = 12(32 cm)2=512 cm2
Area of 1st shade = Area of 2nd shade
=512 cm22=256 cm2
Therefore, the area of paper required in each shape is 256 cm2
For IIIrd triangle
Semi-perimeter, s=(6+6+8)2=10 cm
By Heron’s formula,
Area of triangle = √s(s−a)(s−b)(s−c)
Area of IIIrd triangle
= √10(10−6)(10−6)(10−8)=(√10×4×4×2)cm2=(4×2√5)cm2=8√5cm2=(8×2.24)cm2=17.92cm2
Area of paper required for IIIrd shade = 17.92 cm2