Question

In each of the figures, find the area of the coloured portion.

Answer 1

(1) Side of the equilateral triangle is 8 cm.
Area of an equilateral triangle is $\frac{\sqrt{3}}{4}{\left(\mathrm{side}\right)}^2$.
∴ Area of the given triangle = $\frac{\sqrt{3}}{4}$ × 8 cm × 8 cm
= 16 $\sqrt{3}$ sq cm


(2) Area of the shaded part in the figure = Area of the triangle – Area of the rectangle
Height of the triangle = 8 cm
Base of the triangle = AC = 20 cm
Area of a right triangle is $\frac{1}{2}$ (Base× Height)
= $\frac{1}{2}$ × 20 cm × 8cm = 80 sq cm

Length of the rectangle = 4 cm
Breadth of the rectangle = 5 cm
Area of the rectangle =Length× Breadth= 4 cm × 5 cm = 20 sq cm

Area of the shaded part = Area of the right triangle - Area of the rectangle = 80 sq cm – 20 sq cm
= 60 sq cm
∴ Area of the shaded part = 60 sq cm

(3) Area of the shaded part in the given figure = Area of the parallelogram – Area of the triangle
Height of the parallelogram is 15 cm.
Base of the parallelogram is 20 cm.
Area of a parallelogram = height × base
= 15 cm × 20 cm
= 300 sq cm
Area of a right triangle = $\frac{1}{2}$ (Base × Height)
= $\frac{1}{2}$ × 15 cm × 20 cm = 150 sq cm
Area of the shaded part in the given figure = Area of the parallelogram - Area of the right triangle
= 300 sq cm – 150 sq cm
∴ Area of the shaded part = 150 sq cm

(4) Area of the shaded part in the given figure = Area of the rectangle – Area of the triangle
Length of the rectangle is 12 cm.
Breadth of the rectangle is 18 cm.
Area of a rectangle = Length × Breadth
= 12 cm × 18 cm = 216 sq cm
Area of a right triangle = $\frac{1}{2}$ (Base×Height)
= $\frac{1}{2}$ × 12 cm × 18 cm = 108 sq cm
Area of the shaded part in the given figure = Area of the rectangle - Area of the triangle
= 216 sq cm – 108 sq cm
∴ Area of the shaded part = 108 sq cm