Mathematics: Geometry and Measurement Flashcards

A right triangle has legs of 5 and 12. What is the length of the hypotenuse?

Answer: 13

By the Pythagorean theorem: c = √(5² + 12²) = √(25 + 144) = √169 = 13.

What is the surface area of a cube with a side length of 4 inches?

Answer: 96 in²

A cube has 6 faces; surface area = 6s² = 6(4²) = 6(16) = 96 in².

An angle measures 130°. What is the measure of its supplement?

Answer: 50°

Supplementary angles sum to 180°, so the supplement = 180° − 130° = 50°.

A map uses a scale of 1 inch = 50 miles. Two cities are 3.5 inches apart on the map. What is the actual distance?

Answer: 175 miles

Actual distance = 3.5 × 50 = 175 miles.

What is the volume of a rectangular prism that is 6 cm long, 4 cm wide, and 3 cm tall?

Answer: 72 cm³

Volume = l × w × h = 6 × 4 × 3 = 72 cm³.

A sector of a circle has a central angle of 90° and a radius of 6 cm. What is the area of the sector? (Use π ≈ 3.14)

Answer: 28.26 cm²

Area of sector = (θ/360°) × πr² = (90/360) × 3.14 × 36 = 0.25 × 113.04 = 28.26 cm².

Two parallel lines are cut by a transversal. If one co-interior (same-side interior) angle is 110°, what is the other?

Answer: 70°

Co-interior angles are supplementary, summing to 180°, so the other angle = 180° − 110° = 70°.