Area of Shapes in the Plane
Primary 4 · Mathematics
Area of Shapes in the Plane
Lesson 5 of 5
30 min
Let's begin
On a hillside farm, the terraces are cut into shapes with two parallel edges, like trapeziums. Umutoni's mother wants to know how much land one terrace has, so she can decide how many bean seeds to buy.
Today you will use what you know about rectangles and triangles to find the area of a rhombus and a trapezium.
A rhombus is a special parallelogram, so base × height works. But there is another neat way that uses its diagonals.
Draw a rectangle around the rhombus. The rectangle's sides are the same lengths as the two diagonals. The rhombus fills exactly half of it.
Area of a rhombus = diagonal × diagonal ÷ 2
Example: a rhombus-shaped badge has diagonals of 10 cm and 6 cm. Area = 10 × 6 ÷ 2 = 60 ÷ 2 = 30 cm².
Take two copies of the same trapezium. Turn one round and fit it next to the other. Together they make a parallelogram.
The parallelogram's base is the two parallel sides added together. So one trapezium is half of (sum of the parallel sides × height).
Area of a trapezium = (sum of the parallel sides) × height ÷ 2
Example: Umutoni's terrace has parallel sides of 12 m and 8 m, and they are 5 m apart. Area = (12 + 8) × 5 ÷ 2 = 20 × 5 ÷ 2 = 100 ÷ 2 = 50 m².
You can also split a trapezium into a rectangle and triangles, find each area, and add them. You will get the same answer.
Tip
Rhombus: diagonal times diagonal, then halve. Trapezium: add the parallel sides, times the height, then halve. Both are "half of a bigger shape".
Work each one in your exercise book first. Then tap Show answer to check.
A rhombus has diagonals of 8 cm and 5 cm. Find its area.
Answer: 20 cm², because 8 × 5 = 40 and 40 ÷ 2 = 20.
A rhombus has a base of 6 m and a height of 4 m. Find its area.
Answer: 24 m², because 6 × 4 = 24 (a rhombus is a parallelogram).
A trapezium has parallel sides of 4 cm and 6 cm and a height of 3 cm. Find its area.
Answer: 15 cm², because (4 + 6) × 3 = 30 and 30 ÷ 2 = 15.
A trapezium-shaped plot has parallel sides of 15 m and 9 m, and a height of 10 m. Find its area.
Answer: 120 m², because (15 + 9) × 10 = 240 and 240 ÷ 2 = 120.
What you learned today
Sources and credits
The diagonal rule for the rhombus and the two-copies picture for the trapezium were written by Ganzaa. The stories, Rwandan examples, diagrams and practice questions were written by Ganzaa.
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