Areas and Distances

The diagram shows three quarters that are joined at vertices to form a right triangle.

Which statement is true?

• The sum of the areas of Region X and Region Y is equal to the area of Region Z.

• The sum of the areas of Region X and Region Y is greater than the area of Region Z.

• The sum of the areas of Region X and Region Z is equal to the area of Region Y.

• The sum of the areas of Region X and Region Z is less than the area of Region Y.

Find the missing length. Round to the nearest hundredth if necessary.

• 11.40 cm

• 10.58 cm

• 9.2 cm

• 8 cm

The manager of a car dealership wants to attach a rope with flags to the top a pole and to a stake in the ground, as shown in the diagram.

Based on the diagram, what is the distance in feet from the top of the pole to the bottom of the stake?

The diagram shows Squares D, E, and F joined at vertices to form a right triangle. Which statement is true?

• The sum of the areas of Square D and Square F is less than the area of Square E.

• The sum of the areas of Square D and Square E is greater than the area of Square F.

• The sum of the areas of Square D and Square F is equal to the area of Square E.

• The sum of the areas of Square D and Square E is equal to the area of Square F.

The diagram shows three squares that are joined at vertices to form a right triangle. Which statement is true?

• The sum of the areas of Square N and Square L is equal to the area of Square K.

• The sum of the areas of Square N and Square L is greater than the area of Square K.

• The sum of the areas of Square N and Square K is equal to the area of Square L.

• The sum of the areas of Square N and Square K is less than the area of Square L.

The diagram shows a right triangle and the lengths of two of its sides in inches.

Which measurement is closest to the value of d in inches?

• 6.3 in

• 4.0 in

• 14.3 in

• 19.8 in

The diagram represents a ramp in the shape of a right triangle and the lengths of two of its sides in feet.

What is the length of the ramp?

The width of a rectangle is 4 feet, and the diagonal length of the rectangle is 13 feet. Which measurement is closest to the length of this rectangle in feet?

• 9 ft

• 17 ft

• 12.4 ft

• 13.6 ft

The length of a rectangular frame is 15 inches, and the width of the frame is 8 inches. What is the length of a diagonal of this frame in inches?

Natasha walked from the library to the grocery store and then to her house. The diagram shows the top view of the locations of these three places and their distances from each other. Which measurement is closest to the shortest distance in miles from Natasha's house to the library?

• 2.6 mi

• 1.9 mi

• 1.4 mi

• 2.3 mi