Grade 6

Area and volume

Flat and solid. Part of below zero and beyond.

Area and volume

Flat and solid · Alberta Grade 6 · maddyhelps.com

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A parallelogram's area is base × height, where the height is measured straight up from the base. A triangle is half of a parallelogram with the same base and height. The volume of a box is length × width × height, in cubic units.

Shape	Area
Parallelogram, base 9 cm, height 4 cm
Triangle, base 10 cm, height 6 cm
Triangle, base 7 cm, height 4 cm
Triangle, base 9 cm, height 5 cm

Volume

A box holds 24 centimetre cubes and is 2 cm tall. Give two different sizes its bottom could be.

For the grown-up

Area and volume

Parallelogram 9 × 4 = 36 cm²; triangle 10 × 6 ÷ 2 = 30 cm²; triangle 7 × 4 ÷ 2 = 14 cm²; triangle 9 × 5 ÷ 2 = 22.5 cm². 5 × 3 × 2 = 30 cm³; 4 × 4 × 4 = 64 cm³; 6 × 2 × 3 = 36 cm³. The bottom must cover 12 cm²: 1 × 12, 2 × 6, 3 × 4.

Cut the triangle off one end of a parallelogram, slide it to the other end, and it becomes a rectangle with the same base and height — that is why base × height works. The 4 × 4 × 4 box is a cube, and 4³ = 64, which is where the word cubed comes from.

Why this matters is on the below zero and beyond page. More sheets