Quadrilateral Lengths & Areas

Name:

Date:

Various quadrilaterals with measurement tools

📐 Part 1: Finding Unknown Lengths

Remember: A quadrilateral (tapawhā) is a four-sided shape. Use the area formula to find missing lengths!

1. A rectangle has an area of 48 cm² and a width of 6 cm. What is its length?

Length = _______ cm

2. A parallelogram has an area of 84 cm² and a base of 12 cm. What is its height?

Height = _______ cm

3. A square has an area of 64 cm². What is the length of each side?

Side length = _______ cm

4. Which equation would you use to find the missing width (w) of a rectangle with area 72 cm² and length 9 cm?

w = 72 + 9

w = 72 ÷ 9

w = 72 × 9

w = 9 - 72

🔧 Part 2: Problem Solving & Scale Drawing

5. A rectangular garden plot has an area of 96 m² and a length of 16 m. Draw the garden to scale on the grid below (use 1 square = 2 m). Label all dimensions.

Width of garden = _______ m

6. A parallelogram-shaped car park has a base of 25 m and an area of 300 m². The council wants to add a fence along the height. How many metres of fencing do they need?

Explain your reasoning: ________________________________________________

Fencing needed = _______ m

7. This composite shape is made of two rectangles. The total area is 110 cm². Find the missing length x.

Top rectangle: 8 cm × 5 cm
Bottom rectangle: x cm × 7 cm

x = _______ cm

💭 Part 3: Mathematical Communication

8. Explain in your own words how you would find the height of a parallelogram if you know its area and base length. Use correct mathematical vocabulary.

9. A rectangular sports field needs to have an area of exactly 5000 m². The length must be 100 m. Is this possible? Show your working and explain your answer.

10. Challenge: Design your own quadrilateral problem involving finding a missing length. Include the area and one other measurement. Then solve it!

Your problem:

Your solution: