6th grade geometry

Example

A triangle has area 16 yd² and base 8 yd. What is its height, in yd?

1. 2 × 16 = 32
2. 32 ÷ 8 = 4 yd

Answer: 4

Example

A parallelogram has base 9 yd and perpendicular height 3 yd. What is its area, in yd²?

1. 9 × 3 = 27 yd²

Answer: 27

Example

In which quadrant is the point (−8, 7)?

1. x is negative, y is positive: quadrant II.

Answer: II

Example

What is the surface area of a cuboid 3 yd × 4 yd × 5 yd, in yd²?

1. 3 × 4 = 12
2. 3 × 5 = 15
3. 4 × 5 = 20
4. 2 × (12 + 15 + 20) = 94 yd²

Answer: 94

Example

A parallelogram has base 4 m and perpendicular height 3 m. Find its area in m².

1. 4 × 3 = 12 m²

Answer: 12

Example

A trapezoid (trapezium) has parallel sides 7 m and 17 m, and height 8 m. Find its area in m².

1. (7 + 17) ÷ 2 = 12
2. 12 × 8 = 96 m²

Answer: 96

Example

An L-shaped room is a 15 m by 7 m rectangle with a 9 m by 3 m rectangle missing from one corner. What is its floor area, in m²?

1. 15 × 7 = 105
2. 9 × 3 = 27
3. 105 − 27 = 78 m²

Answer: 78

Example

Point A is (4, −3). Point B is directly below A, 9 units away. What are the coordinates of B? Type them like (2, −3).

1. −3 − 9 = −12
2. (4, −12)

Answer: (4, −12)

Example

Reflect (1, 8) in the y-axis, then reflect the result in the x-axis. Where does it end up?

1. (1, 8) → (−1, 8) → (−1, −8)

Answer: (−1, −8)

Example

A box measures 2.5 cm by 3 cm by 3 cm. What is its volume, in cm³?

1. 2.5 × 3 = 7.5
2. 7.5 × 3 = 22.5 cm³

Answer: 22.5

Example

Find the surface area of a cuboid 4 cm long, 4 cm wide and 9 cm tall, in cm².

1. 4 × 4 = 16, 4 × 9 = 36, 4 × 9 = 36
2. 2 × (16 + 36 + 36) = 176 cm²

Answer: 176

Example

A net is made of 6 equal squares. Which solid does it fold into?

1. 6 equal squares → cube

Answer: cube