Diagnostic Test

A composite object consists of a right rectangular prism and a right triangular prism joined together. Which of the following would you need to subtract when calculating the total surface area?

• The area of the shared face between the two solids

• The volume of each solid

• The height of the triangular prism

• The perimeter of the rectangular prism

What is the total surface area of a composite object made from a right rectangular prism (10 cm × 4 cm × 3 cm) and a right cylinder (diameter = 4 cm, height = 6 cm) placed on top, centered on the larger face? (Use π ≈ 3.14)

• 188.48 cm²

• 150.72 cm²

• 200.32 cm²

• 175.60 cm²

Which of the following triangles is not a right triangle?

• Sides 6 cm, 8 cm, 10 cm

• Sides 5 cm, 12 cm, 13 cm

• Sides 3 cm, 4 cm, 6 cm

• Sides 9 cm, 12 cm, 15 cm

Using the Pythagorean Theorem, find the length of the missing side of a right triangle if one leg is 7 cm and the hypotenuse is 25 cm.

• 24 cm

• 18 cm

• 20 cm

• 22 cm

A construction worker uses a 3:4:5 triangle to check if a corner of a structure is square. What is the total length of rope needed if each unit of the ratio equals 0.5 meters?

• 6 meters

• 7.5 meters

• 5 meters

• 8 meters

Describe a real-world application of the Pythagorean theorem.

• Calculating the distance between two points on a map

• Determining the area of a circle

• Finding the volume of a cylinder

• Measuring the angle of a triangle

A person stands 50 meters from a building. The angle of elevation from the ground to the top of the building is 60°. What is the approximate height of the building?

• 86.6 meters

• 43.3 meters

• 50 meters

• 75 meters

A ladder leans against a wall forming two right triangles. If the height from the ground to the top of the ladder is 6 m, and the base is 2 m from the wall, what is the length of the ladder?

• 8 m

• 6.32 m

• 4 m

• 10 m

Find the angle between the ladder and the ground if the height from the ground to the top of the ladder is 6 m, and the base is 2 m from the wall.

• 60 degrees

• 30 degrees

• 45 degrees

• 70 degrees

A mountain trail zigzags up a slope forming two right triangles. What is the total horizontal distance traveled if each triangle has a base of 30 m and 45 m respectively, and both have a height of 20 m?

• 75 m

• 60 m

• 90 m

• 100 m