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Formulae Exploration Worksheet

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Formulae Exploration Worksheet

Use the formulae reference when you need it. For calculation questions, show your substitution and include the correct units.

Formulae reference

Rectangle perimeter: P = 2l + 2w. Triangle perimeter: P = a + b + c. Rectangle area: A = l × w. Triangle area: A = ½ × b × h. Trapezoid area: A = ½ × (sum of parallel sides) × perpendicular height. Rectangular prism volume: V = l × w × h. Triangular prism volume: V = ½ × b × h × length. Perimeter is a distance, area is measured in square units, and volume is measured in cubic units.

Formulae knowledge

Match each measurement term to its meaning.

1.Complete these formulae: rectangle area A = × ; triangle area A = ½ × × ; rectangular prism volume V = × × .

2.Why is the area of a triangle calculated using one-half times its base times its perpendicular height?

A triangle has three sides, so its area is divided by two.
A triangle has half the area of a rectangle with the same base and height.
Every area formula includes one-half.
The height of every triangle is half its base.

3.Choose every formula below that uses both a base and a height.

Rectangle perimeter: P = 2l + 2w
Triangle area and triangular prism volume: A = ½ × b × h; V = ½ × b × h × length
Triangle perimeter: P = a + b + c

Substitute and calculate

Write the formula, substitute the measurements and include units in your answer.

4.A rectangular deck on a ferry is 9 m long and 4 m wide. Calculate its perimeter and area.

5.A triangular sign has a base of 8 cm and a perpendicular height of 7 cm. Find its area.

6.A storage box is a rectangular prism measuring 12 cm by 5 cm by 4 cm. Calculate its volume.

7.A triangular prism has a triangular end with base 6 m and perpendicular height 5 m. The prism is 9 m long. Find its volume.

8.A ferry terminal waiting area is 18 m long and 11 m wide. New flooring costs $24 per square metre. What is the total flooring cost?

Extend your thinking

Use what you know about area and volume to solve each problem.

9.A long pool has a trapezoidal cross-section. Its parallel sides are 3 m and 5 m, its perpendicular height is 2 m, and it is 16 m long. Write a volume formula using these measurements, then calculate the volume.

10.A rectangular prism measures 12 cm long, 5 cm wide and 4 cm high. If only its length is doubled to 24 cm, what is its new volume, and how does it compare with the original volume? Explain using the volume formula.