Two-Dimensional Geometry

The sign measures 18 inches across in diameter. Which measurement is closest to the area of the sign in square inches?

Answer explanation

The formula to find the area of a circle is pi times radius squared. We must first find the radius by dividing the diameter by 2. Then we need to multiply the radius times itself, then times 3.14.

A triangle is inscribed in a rectangle, as shown below. What is the area of the shaded region?

Answer explanation

First find the area of the triangle by multiplying the base and height then dividing by 2. Next, find the area of the rectangle by multiplying the base and height. Because are two shapes are different colors, you then need to subtract the two areas to find your answer.

Using various puzzle pieces, Marco forms the figure pictured. What is the best estimate of the area of the figure?

Answer explanation

First find the area of the semicircle. The diameter is 8 so we need to cut that in half to find a radius of 4. Then we multiply the radius by itself and then times 3.14. From there we must divide by 2 since it is a half circle. For the triangle, we must subtract 4 from the base since 16 measures the base and the radius of the circle. Then multiply that by the height and then divide by 2. Finally, we must add our two areas together since the two shapes are the same color.

A puzzle is shown below. Which of the following is the closest to the area of the shaded portions of the puzzle?

Answer explanation

The shape of the shaded region is a parallelogram. To find the area of a parallelogram, we just multiply base times height. Each square is 2 cm and the base is a total of 5 squares and the height is a total of 3.

Which of the following equations can be used to find the missing angle, x, in the triangle below?

• x + 84 = 180

• x + 84 = 360

• x + 42 = 90

• x + 42 =180

Answer explanation

The three angles of a triangle must add up to 180. To write an equation, you just add the three angles given and make it equal to 180.

Janice is painting a portion of a gymnasium court. If Janice paints the shaded area, then how many square feet will she paint?

Answer explanation

First, find the area of the rectangle by multiplying the base and height. Next, we have two semicircles which will make one whole circle. To find the area of the circle, we must first divide the diameter by 2 to find the radius, then multiply the radius by itself and that answer by pi (3.14). Then, since the shapes are different colors, we will subtract the two areas to find the area of the shaded region.

Angle ABC and angle CBD are complementary. What is the value of x?

• 64 degrees

• 52 degrees

• 90 degrees

• 26 degrees

Answer explanation

Complementary angles add up to 90 degrees. If one angle is 38 degrees, subtract that from 90 to find the degree of the other angle. That angle is equal to 2x, so divide the degrees by 2 to find the value of x.

A circular rug has a radius of 4 feet. Which of the following is closest to the number of square inches the rug covers?

Answer explanation

The covering of the rug refers to it's area. To find the area of a circle, you multiply the radius by itself, then multiply that by pi (3.14).

A round clock is shown below. Which of the following is closest to the number of inches around the clock?

• 20.8 in

• 43.36 in

• 16.2 in

• 34.54 in

Answer explanation

To find the measurement around the clock, we are looking for the circumference of the circle. To find circumference, we multiply pi (3.14) times diameter.

Find the area of the trapezoid.