Question

13.
find the area of the shape
a) 10.28 sq in
b) 16.56 sq in
c) 7.14 sq in
find the area of the shaded region
a) 112
b) 784
c) 672
d) 560

Explanation:

First Shape (Top)

Step1: Identify shape components

The shape is a square plus a full circle (the two half-circles combine to one full circle with radius $r=2$ in, and the square has side length $2$ in).

Step2: Calculate square area

Area of square: $A_{square} = s^2 = 2^2 = 4$ sq in

Step3: Calculate circle area

Area of circle: $A_{circle} = \pi r^2 = \pi (2)^2 = 4\pi \approx 12.56$ sq in

Step4: Find total area

Total area = $A_{square} + \frac{1}{2}A_{circle} + \frac{1}{2}A_{circle} = 4 + 6.28 = 10.28$ sq in

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Second Shape (Bottom, #13)

Step1: Calculate area of parallelogram

Area of parallelogram: $A_{para} = b \times h = 32 \times 21 = 672$

Step2: Calculate area of shaded rectangle

Area of rectangle: $A_{rect} = l \times w = 16 \times 7 = 112$
(Note: The shaded region is the rectangle itself, so this is the final area.)

Answer:

a) 10.28 sq in