Find the area of the shape shown in figure, all dimensions are in mm²

Concept:

The area of the shape = (Area of the trapezium) + (Area of the semi-circle)

Area of the trapezium = \(\frac{1}{2}\) × (sum of the parallel sides) × height

Area of the semi-circle = \(\frac{\pi~\times~r^2}{2}\)

Calculation:

Given:

Lengths of the parallel sides are 50 and 80 mm

Diameter = Height = 70 mm, ∴ Radius of the semi-circle = 35 mm

∵ Area of the trapezium = \(\frac{1}{2}\) × (sum of the parallel sides) × height

⇒ Area of the trapezium = \(\frac{1}{2}\) × (50+ 80) × 70 = 4550 mm²

Area of the semi-circle = \(\frac{\pi~\times~r^2}{2}\) = \(\frac{\pi~\times~{35}^2}{2}\) = 1925 mm²

∵ The area of the shape = (Area of the trapezium) + (Area of the semi-circle)

⇒ The area of the shape = 1925 + 4550 = 6475 mm²