Measurement and Geometry Flashcards

A trapezoid has bases of 8 cm and 12 cm, and a height of 5 cm. What is its area?

Answer: 50 cm²

Area of a trapezoid = ½ × (b₁ + b₂) × h = ½ × (8 + 12) × 5 = ½ × 20 × 5 = 50 cm².

A triangle is reflected across the y-axis. The original triangle has a vertex at (4, −2). Where is the corresponding vertex after reflection?

Answer: (−4, −2)

Reflecting across the y-axis changes the sign of the x-coordinate only: (4, −2) becomes (−4, −2).

A rectangular room is 12 feet by 10 feet. How many square yards of carpet are needed to cover the floor? (1 yard = 3 feet)

Answer: 13.33 yd²

Room area = 12 × 10 = 120 ft²; converting: 120 ÷ 9 = 13.33 yd² (since 1 yd² = 9 ft²).

Which set of side lengths could form a right triangle?

Answer: 5, 12, 13

5² + 12² = 25 + 144 = 169 = 13², confirming (5, 12, 13) is a Pythagorean triple.

A shape is dilated by a scale factor of 3. If the original shape had an area of 8 cm², what is the area of the dilated shape?

Answer: 72 cm²

When a shape is dilated by scale factor k, the area changes by k², so new area = 8 × 3² = 8 × 9 = 72 cm².

A cone has a radius of 4 cm and a height of 9 cm. What is its volume? (Use π ≈ 3.14)

Answer: 150.72 cm³

Volume of a cone = (1/3) × π × r² × h = (1/3) × 3.14 × 16 × 9 = 150.72 cm³.

Two supplementary angles are in a ratio of 2:3. What are the two angle measures?

Answer: 72° and 108°

Supplementary angles sum to 180°; with ratio 2:3, the parts are 2x + 3x = 180°, so x = 36°, giving 72° and 108°.