Question
By splitting the following figures into rectangles, find their areas (all measures are given in meters):
✓
Answer
(a) Splitting the given figure into I, II, III, and IV rectangles as shown in the figure below, we get
Here, the area of rectangle I = length × breadth
= 4 cm × 3 cm
= 12 sq. cm
Area of rectangle II = length × breadth
= 3 cm × 2 cm
= 6 sq. cm
Area of rectangle III = length × breadth
= 4 cm × 1 cm
= 4 sq. cm
Area of rectangle IV = length × breadth
= 3 cm × 2 cm
= 6 sq. cm
The total area of the whole figure = 12 sq. cm + 6 sq. cm + 4 sq. cm + 6 sq. cm = 28 sq. cm.
Therefore, the total area of Figure (a) is 28 sq. cm.
(b) Similarly, by splitting figure (b) into I, II, and III rectangles as shown in the figure below, we get
Area of the rectangle I = length × breadth
= 3 cm × 1 cm
= 3 sq. cm
Area of rectangle II = length × breadth
= 3 cm × 1 cm
= 3 sq. cm
Area of rectangle III = length × breadth
= 3 cm × 1 cm
= 3 sq. cm
The total area of the figure = 3 sq. cm + 3 sq. cm + 3 sq. cm = 9 sq. cm.
Therefore, the total area of Figure (b) is 9 sq. cm.
Here, the area of rectangle I = length × breadth
= 4 cm × 3 cm
= 12 sq. cm
Area of rectangle II = length × breadth
= 3 cm × 2 cm
= 6 sq. cm
Area of rectangle III = length × breadth
= 4 cm × 1 cm
= 4 sq. cm
Area of rectangle IV = length × breadth
= 3 cm × 2 cm
= 6 sq. cm
The total area of the whole figure = 12 sq. cm + 6 sq. cm + 4 sq. cm + 6 sq. cm = 28 sq. cm.
Therefore, the total area of Figure (a) is 28 sq. cm.
(b) Similarly, by splitting figure (b) into I, II, and III rectangles as shown in the figure below, we get
Area of the rectangle I = length × breadth
= 3 cm × 1 cm
= 3 sq. cm
Area of rectangle II = length × breadth
= 3 cm × 1 cm
= 3 sq. cm
Area of rectangle III = length × breadth
= 3 cm × 1 cm
= 3 sq. cm
The total area of the figure = 3 sq. cm + 3 sq. cm + 3 sq. cm = 9 sq. cm.
Therefore, the total area of Figure (b) is 9 sq. cm.
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