Two make a parallelogram
Area of a triangle
Make a copy
The area of a parallelogram is bh. Now take a triangle and make an exact copy of it. Two congruent copies of a triangle can be fitted together.
Two congruent copies of a triangle fit together to make a parallelogram. How does the area of the triangle compare with that parallelogram?
What this lesson covers
The idea
Two congruent copies of a triangle fit together to make a parallelogram, so the area of a triangle is (1/2)(base × height) = (1/2)bh.
Make a copy
The area of a parallelogram is bh. Now take a triangle and make an exact copy of it. Two congruent copies of a triangle can be fitted together.
Two congruent copies of a triangle fit together to make a parallelogram. How does the area of the triangle compare with that parallelogram?
- It is half of it
- It is the same as it
- It is a third of it
Turn the copy
Turn the orange copy about the purple dot, for each triangle. What shape do the two copies make?
Half of bh
Two congruent copies of a triangle fit together to make a parallelogram, so the area of a triangle is half of base × height, that is half of b × h.
The copy is turned through a half-turn about the middle of one side. The equal angles where the copies meet show that opposite sides are parallel, so the pieces make a parallelogram with the same base b and height h. This works for any triangle: pointed, right-angled or wide.
Notes
Two congruent copies of a triangle make a parallelogram, so the area of a triangle = half of base × height.
Check yourself
A triangle has base 10 cm and height 6 cm. What is its area?
Answer: 30 cm²
Area = 1/2 × 10 × 6 = 1/2 × 60 = 30 cm².
A triangle has area 36 cm² and base 9 cm. What is its height?
Answer: 8 cm
bh = 2 × 36 = 72, so h = 72 ÷ 9 = 8 cm.
A triangle and a parallelogram have the same base and the same height. The triangle's area is…
A right-angled triangle has two short sides of 7 cm and 12 cm. What is its area?
Answer: 42 cm²
Area = 1/2 × 7 × 12 = 1/2 × 84 = 42 cm².
- the same as the parallelogram's area. Two copies of the triangle are needed to make the parallelogram. One triangle is half of it.
- half the parallelogram's area — correct. Yes. Two copies of the triangle make a parallelogram like that one.
- twice the parallelogram's area. The triangle fits inside the parallelogram twice over, so it is the smaller one.