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Find the Area of the figure below, composed of a rectangle with two semicircles removed. Round to the nearest tenths place.

Find the Area of the figure below, composed of a rectangle with two semicircles removed. Round to the nearest tenths place.

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Find the direction angle of a vector

Full solution

Q. Find the Area of the figure below, composed of a rectangle with two semicircles removed. Round to the nearest tenths place.

Identify Dimensions and Radius: Step $1$ : Identify the dimensions of the rectangle and the radius of the semicircles. Assume the rectangle has a length of $10\,\text{cm}$ and a width of $6\,\text{cm}$ . The radius of each semicircle is $3\,\text{cm}$ (half of the width of the rectangle).
Calculate Rectangle Area: Step $2$ : Calculate the area of the rectangle. Area of rectangle = length $\times$ width = $10\, \text{cm}$ $\times$ $6\, \text{cm}$ = $60\, \text{cm}^2$ .
Calculate Semicircle Area: Step $3$ : Calculate the area of one semicircle. Area of a semicircle = $(\pi \times \text{radius}^2) / 2$ . For one semicircle, Area = $(\pi \times 3^2) / 2 = (\pi \times 9) / 2 \approx 14.1 \, \text{cm}^2$ .
Calculate Total Semicircles Area: Step $4$ : Calculate the total area of the two semicircles. Total area of semicircles = $2 \times 14.1 \, \text{cm}^2 = 28.2 \, \text{cm}^2$ .
Find Figure Area: Step $5$ : Subtract the area of the semicircles from the area of the rectangle to find the area of the figure. Area of figure = Area of rectangle - Total area of semicircles = $60 \, \text{cm}^2 - 28.2 \, \text{cm}^2 = 31.8 \, \text{cm}^2$ .

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