In Figure 1, the dimension of the rectangle inscribed in a circle of diameter 14 m is given as 8 m x 5 m…

Question

In Figure 1, the dimension of the rectangle inscribed in a circle of diameter 14 m is given as 8 m x 5 m. Find the area of the shaded portion. (Take π = 22/7)

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5.

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6.

a) In Figure 1, the dimension of the rectangle inscribed in a circle of diameter $|AO| = 14 \text{ m}$ is given as $8 \text{ m} \times 5 \text{ m}$ . Find the area of the shaded portion. (Take $\pi = \frac{22}{7}$ )

Determine the radius of the circle.
The diameter of the circle is $14 \text{ m}$ .
The radius $r$ is half of the diameter.
$r = \frac{\text{diameter}}{2} = \frac{14 \text{ m}}{2} = 7 \text{ m}$
Calculate the area of the circle.
The formula for the area of a circle is $A_{circle} = \pi r^2$ .
$A_{circle} = \frac{22}{7} \times (7 \text{ m})^2$ $A_{circle} = \frac{22}{7} \times 49 \text{ m}^2$ $A_{circle} = 22 \times 7 \text{ m}^2 = 154 \text{ m}^2$
Calculate the area of the inscribed rectangle.
The dimensions of the rectangle are $8 \text{ m}$ by $5 \text{ m}$ .
The formula for the area of a rectangle is $A_{rectangle} = \text{length} \times \text{width}$ .
$A_{rectangle} = 8 \text{ m} \times 5 \text{ m} = 40 \text{ m}^2$
Calculate the area of the shaded portion.
The shaded portion is the area of the circle minus the area of the rectangle.
$A_{shaded} = A_{circle} - A_{rectangle}$ $A_{shaded} = 154 \text{ m}^2 - 40 \text{ m}^2$ $A_{shaded} = 114 \text{ m}^2$
The area of the shaded portion is $\boxed{114 \text{ m}^2}$ .

In Figure 1, the dimension of the rectangle inscribed in a circle of diameter 14 m is given as 8 m x 5 m. Find the area of the shaded portion. (Take π = 22/7)

Step-by-step solution

Determine the radius of the circle.

Calculate the area of the circle.

Calculate the area of the inscribed rectangle.

Calculate the area of the shaded portion.

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