Cut and slide
Area of a parallelogram
A leaning shape
A rectangle with sides a and b has area ab, because it is a × b unit squares. A parallelogram leans over, so its area is harder to see.
Can we cut a parallelogram and rearrange the pieces into a rectangle?
What this lesson covers
The idea
A parallelogram can be transformed into a rectangle with the same base b and height h, so its area is base × height = bh.
A leaning shape
A rectangle with sides a and b has area ab, because it is a × b unit squares. A parallelogram leans over, so its area is harder to see.
Can we cut a parallelogram and rearrange the pieces into a rectangle?
- Yes, cut a triangle off one end and move it to the other end
- No, a leaning shape can never become a rectangle
- Only if all its sides are equal
Cut and slide
Slide the orange piece to the other end. Do it for each parallelogram. Does the shape stay the same size?
Same area, new shape
A parallelogram can be transformed into a rectangle with the same base b and the same height h, so its area is base × height = bh.
Cut off the triangle at one end, along the height, and slide it to the other end. Nothing is added and nothing is lost, so the two shapes have the same area, though they look different. The height h is the straight-up distance between the two parallel sides, not the slanted side.
Notes
A parallelogram can be turned into a rectangle with the same base b and height h, so its area = base × height = bh.
Check yourself
A parallelogram has base 9 cm and height 5 cm. What is its area?
Answer: 45 cm²
Area = bh = 9 × 5 = 45 cm².
A parallelogram has base 8 m and area 56 m². What is its height?
Answer: 7 m
h = 56 ÷ 8 = 7 m.
A parallelogram has base 10 cm, a slanted side of 6 cm and height 4 cm. What is its area?
Two parallelograms have the same base and the same height, but one leans over more. Their areas are…
- 60 cm². 6 cm is the slanted side. The area uses the height, 4 cm.
- 40 cm² — correct. Yes. Area = base × height = 10 × 4. The height is the straight-up distance.
- 20 cm². That is half of 40. The parallelogram becomes a whole rectangle 10 by 4, so nothing is halved.
- larger for the one that leans more. The area depends only on b and h, not on how much the shape leans.
- smaller for the one that leans more. The area depends only on b and h, not on how much the shape leans.
- equal — correct. Yes. Each one can be cut and slid into the same rectangle b by h.