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BartSMP [9]
3 years ago
9

The stadium has a form of a rectangle with two semicircles attached to the short sides. The long side of a rectangle is 2 times

longer than the short one. Construct the expression for the area of the stadium in terms of x, where x denotes a shorter side of the rectangle

Mathematics
1 answer:
mr Goodwill [35]3 years ago
4 0

Answer: 2x^2+\frac{\pi x^2}{4}

Step-by-step explanation:

The area of a rectangle can be calculated with this formula:

A_r=lw

Where "l" is the lenght and "w" is the width.

The area of a semi-circle can be found with this formula:

A_{sc}=\frac{\pi r^2}{2}

Where "r" is the radius.

 Let be "x" the shorter side of the rectangle (which is also the diameter of the semi-circle).

Based on the information given in the exercise, you know that:

w=x\\\\l=2x

Since the radius is half the diameter:

r=\frac{x}{2}

Observe the figure attached, which shows the stadium.

The area of the stadium is the sum of the areas of the semi-cirlcles and the rectangle.

Therefore, you can construct the following expression for the area of the stadium is terms of "x":

(2x)(x)+\frac{\pi (\frac{x}{2})^2}{2}+\frac{\pi (\frac{x}{2})^2}{2}

Simplifying it, you get:

(2x)(x)+\frac{\frac{\pi x^2}{4}}{2}+\frac{\frac{\pi x^2}{4}}{2}=2x^2+\frac{\pi x^2}{4}

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