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Area of a parallelogram: base times height
Discover Mathematics P6: Term 2, Unit 12, Lessons 1–2
GoalFind the area of a parallelogram as base times height, using the perpendicular height.
New words
parallelogram · a four-sided shape with two pairs of parallel sidesbase · the side we choose to measure fromheight · the perpendicular distance from the base to the opposite side
Explanation
Cut a triangle from one end of a parallelogram, slide it to the other end, and you get a rectangle with the same area. The rectangle’s length is the base of the parallelogram and its width is the HEIGHT of the parallelogram. So the area of a parallelogram is base × height. The height is measured at a right angle to the base, drawn as a dashed line. It is NOT the slanted side. A rectangle and a square are special parallelograms whose slanted side is already the height. Area is measured in square units: cm² or m².
ƒFormula
Area of a parallelogram = base × height A = b × h
The height is perpendicular to the base. It is not the slanted side.
Worked examples
The base is 8 cm and the height is 4 cm (the slanted side is 5 cm but we do not use it). Area = 8 × 4 = 32 cm².
Cut and slide: the parallelogram with base 8 cm and height 4 cm becomes a rectangle 8 cm by 4 cm. Both have area 32 cm².
A garden is a parallelogram with base 12 m and height 5 m, so its area is 12 × 5 = 60 m². A square with side 6 cm has base 6 and height 6, so its area is 6 × 6 = 36 cm².
Class activity
Cut and slide. Draw a parallelogram on paper, cut it out, cut a right triangle from one end and slide it to the other end. Check that you get a rectangle. Measure its sides and find the area.
Practice
1
A parallelogram has base 9 cm and height 7 cm. Find its area.
9 × 7 = 63 cm².
2
A parallelogram has base 15 m and height 4 m. Find its area.
15 × 4 = 60 m².
3
A parallelogram has base 10 cm, slanted side 13 cm and height 12 cm. Find its area.
Use the height, not the slanted side: 10 × 12 = 120 cm².
4
A square has side 7 cm. Find its area using base × height.
7 × 7 = 49 cm².
5
Salma finds the area of the parallelogram in the picture as 8 × 5 = 40 cm². What is her mistake? What is the area?
She used the slanted side 5 cm. The height is 4 cm, so the area is 8 × 4 = 32 cm².