Area of Shapes in the Plane
Primary 4 · Mathematics
Area of Shapes in the Plane
Lesson 4 of 5
25 min
Let's begin
Niyonzima's father has a field shaped like a leaning rectangle, a parallelogram. "Can we find its area like a rectangle?" Niyonzima asks. "Almost," says his father, "but we must be careful which length we use."
Draw a parallelogram on squared paper. Cut off the triangle at one end along a straight-up line. Slide it to the other end. The parallelogram becomes a rectangle, and no area is lost or added.
The rectangle has the same base (6) and the same height (3) as the parallelogram. So the area is 6 × 3 = 18 square units.
Area of a parallelogram = base × height
The height is the straight-up distance between the two parallel sides. It meets the base at a right angle.
A parallelogram has a base of 9 m, a slanting side of 5 m and a height of 4 m.
Tip
Stand the height up straight. A parallelogram is a rectangle that has been pushed over. Its area is base × the straight-up height, never the slanting side.
Work each one in your exercise book first. Then tap Show answer to check.
A parallelogram has a base of 7 cm and a height of 3 cm. Find its area.
Answer: 21 cm², because 7 × 3 = 21.
A parallelogram has a base of 10 m, a slanting side of 6 m and a height of 5 m. Find its area.
Answer: 50 m², because 10 × 5 = 50. The 6 m side is not needed.
A rectangle and a parallelogram both have a base of 8 cm and a height of 4 cm. Compare their areas.
Answer: They are equal: both are 32 cm².
A parallelogram has an area of 40 cm² and a base of 8 cm. What is its height?
Answer: 5 cm, because 8 × 5 = 40.
What you learned today
Sources and credits
The stories, Rwandan examples, diagrams and practice questions were written by Ganzaa.
Quick check
A parallelogram has base 8 m, slanting side 5 m and height 3 m. What is its area?
