Question

Find the area of the shaded portion in the figure given below: 

• A. 160 m²
• B. 144 m²
• C. 169 m²
• D. 100 m²

Hint:

When calculating area of combined shapes, always subtract the overlapped region once to avoid double counting.

Answer 1

The Correct Option is B

The figure is a rectangle with dimensions 30 m length and 10 m height. The shaded portion is made by the overlap of two shaded rectangles: one vertical of width 4 m and height 10 m, and one horizontal of height 4 m and length 30 m.
Step 1: Calculate the area of the vertical shaded rectangle:
Width = 4 m, Height = 10 m
Area = \(4 \times 10 = 40 \, m^2\)
Step 2: Calculate the area of the horizontal shaded rectangle:
Height = 4 m, Length = 30 m
Area = \(4 \times 30 = 120 \, m^2\)
Step 3: The shaded region is the union of these two rectangles. Since these two shaded parts overlap in a small rectangle, we need to subtract the overlapped area once to avoid double counting.
Step 4: Find the overlapped area:
Overlap dimensions = Width of vertical rectangle \(4\,m\) × Height of horizontal rectangle \(4\,m\)
Overlap area = \(4 \times 4 = 16 \, m^2\)
Step 5: Total shaded area = Area of vertical + Area of horizontal - Overlapped area
= \(40 + 120 - 16 = 144 \, m^2\)
Hence, the area of the shaded portion is \(144 \, m^2\).