Measurement and Geometry Flashcards

The length of a rectangle is three times its width. If the perimeter is 48 inches, what is the width?

Answer: 6 inches

Let width = w; then 2(w + 3w) = 48 → 8w = 48 → w = 6 inches.

A circle has an area of 78.5 cm². What is its radius? (Use π ≈ 3.14)

Answer: 5 cm

Area = πr² → 78.5 = 3.14r² → r² = 25 → r = 5 cm.

Triangle ABC has angles A = 45° and B = 75°. What is the measure of angle C?

Answer: 60°

The sum of angles in a triangle is 180°; C = 180° − 45° − 75° = 60°.

A figure is reflected across the y-axis. If a vertex was originally at (3, −2), where is the new vertex?

Answer: (−3, −2)

Reflecting across the y-axis negates the x-coordinate: (3, −2) → (−3, −2).

A square pyramid has a square base with side length 6 m and a height of 8 m. What is its volume?

Answer: 96 m³

Volume = (1/3) × base area × height = (1/3) × 36 × 8 = 96 m³.

Two parallel lines are cut by a transversal. One alternate interior angle measures 72°. What is the measure of the other alternate interior angle?

Answer: 72°

Alternate interior angles are congruent when formed by parallel lines and a transversal, so the angle is also 72°.

Which formula gives the surface area of a rectangular prism with length l, width w, and height h?

Answer: 2lw + 2lh + 2wh

Surface area = 2lw + 2lh + 2wh accounts for all six rectangular faces of the prism.