Question

Find the area of the given irregular shape.
[4 marks]

Answer 1

To find the area of the irregular shape, we will add up the area of the shapes that come together to form this irregular shape:
Let us find the area of each shape first.

Area of rectangle 'P' = Length × Width = 6 × 8 = 48 sq. units
[0.5 marks]

Area of semicircle 'Q' = <!--td {border: 1px solid #cccccc;}br {mso-data-placement:same-cell;}--> $\frac{\pi r^2}{2}$ = $\frac{(3.14\times 52)}{2}$ (taking π = 3.14 and, the diameter of the semicircle as 10 after using the Pythagoras theorem in figure R)

⇒ Area of semicircle 'Q' = $\frac{(3.14\times 52)}{2}$ = 39.25 sq. units
[1 Mark]

Area of the triangle 'R' = $\frac{1}{2}$ × Base × Height
⇒ Area of the triangle 'R' = $\frac{1}{2}$ × 8 × 6 = 24 sq. units
[0.5 Marks]

Area of rectangle 'S' = Length × Breadth = 6 × 8 = 48 sq. units
[0.5 Marks]

Now, let us find the area of the irregular shape using the area of the regular shapes:

Area of the given irregular shape = Area of the rectangle 'P' + Area of the semicircle 'Q' + Area of the triangle 'R' + Area of the rectangle 'S'.

⇒ Area of the given irregular shape = 48 + 39.25 + 24 + 48 = 159.25 sq. units.

Therefore, the area of the given irregular shape is 159.25 sq. units.
[1.5 marks]