The figure shows 4 similar right-angled triangles arranged to form a big square which encloses a circle. The midpoints of the 4 sides of the big square touch the circumference of the circle. The two sides which form the right angle of each triangle are 32 cm and 24 cm respectively. Find the area of the shaded parts. (Take π = 3.14)
Difference in the length of the base and height of each triangle
= 32 - 24
= 8 cm
Area of the small square
= 8 x 8
= 64 cm
2 Area of the 4 triangles
=
12 x 24 x 32 x 4
= 1536 cm
2 Area of the big square
= 1536 + 64
= 1600 cm
2 Length of the big square
= √1600
= 40 cm
Radius of the big circle
= 40 ÷ 2
= 20 cm
Area of the big circle
= 3.14 x 20 x 20
= 1256 cm
2
Area of the 4 boomerangs
= 1600 - 1256
= 344 cm
2 Area of the shaded parts
= Area of the 2 boomerangs
= 344 ÷ 2
= 172 cm
2 Answer(s): 172 cm
2