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# Area of Geometric Figures Practice Questions

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Updated on Oct 3, 2011

To review these concepts, go to Area of Geometric Figures Study Guide.

## Area of Geometric Figures Practice Questions

### Practice

1. Find the area.

2. Find the area.

3. Find the area.

4. Find the area of the irregular figure. Use 3.14 for π.

### Solutions

1. The area of a circle is A = πr2, where π is a constant, and r is the radius of the circle. The problem gives the diameter to be 10 in. The radius, 5 inches, is one-half of the length of the diameter. Using the formula A = π × 5 × 5, the area is 25π in2.
2. Opposite sides of a rectangle are congruent. Use this fact and algebra to solve for the variable x. Then find the dimension's length of the side of the rectangle. Multiply this by the side of length 12 to get the area:

Set up an equation: x – 5 = 112 – 8x

Add 8x to both sides: x – 5 + 8x = 112 – 8x + 8x

Combine like terms: 9x – 5 = 112

Add 5 to both sides: 9x – 5 + 5 = 112 + 5

Combine like terms: 9x = 117

Divide both sides by 9:   x = 13

Use this value to find the side of the rectangle: x – 5 = 13 – 5 = 8 m. The area is 8 ×12 = 96 m2.

3. The area of a trapezoid is , where A stands for area, b1 and b2 are the lengths of the parallel bases, and h is the height, the length of the segment perpendicular to the bases. In this trapezoid, the height = 10 m, because it is perpendicular to the bases. The bases are the parallel sides, 16 m and 10 m. Substitute the given information into the formula: to get . Multiply all terms on the right together to yield an area of 130 m2.
4. This figure is a rectangle and one-half of a circle. The area will be A = Arectangle + (Acircle divided by 2): A = bh + πr2 ÷ 2. The radius is one-half of the width of the rectangle; the radius is 7: 238 + 76.93 = 314.93 in2.

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