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

**Area of Geometric Figures Practice Questions **

**Practice**

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

**Solutions**

- The area of a circle is
*A*= π*r*^{2}, 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 in^{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 – 8*x*Add 8

*x*to both sides:*x*– 5 + 8*x*= 112 – 8*x*+ 8*x*Combine like terms: 9

*x*– 5 = 112Add 5 to both sides: 9

*x*– 5 + 5 = 112 + 5Combine like terms: 9

*x*= 117Divide both sides by 9:

*x*= 13Use this value to find the side of the rectangle:

*x*– 5 = 13 – 5 = 8 m. The area is 8 ×12 = 96 m^{2}. - The area of a trapezoid is , where A stands for area,
*b*_{1}and*b*_{2}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 m^{2}. - This figure is a rectangle and one-half of a circle. The area will be
*A*=*A*_{rectangle}+ (*A*_{circle}divided by 2):*A*=*bh*+ π*r*^{2}÷ 2. The radius is one-half of the width of the rectangle; the radius is 7: 238 + 76.93 = 314.93 in^{2}.

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