3
Missing base or height from a known area
Discover Mathematics P6: Term 2, Unit 12, Lessons 1–2
GoalFind a missing base or height when the area is known.
New words
missing · not known yetinverse · the operation that undoes another, such as division for multiplicationarea expression · a short rule for area, such as b × h
Explanation
The area formula connects three numbers, so if we know two of them we can find the third by the inverse operation. For a parallelogram, A = b × h, so b = A ÷ h and h = A ÷ b. For a triangle, A = b × h ÷ 2, so b × h = A × 2, and then b = A × 2 ÷ h and h = A × 2 ÷ b. Do not forget to double the area first for a triangle. Check your answer by putting it back into the formula. The units match: cm² for the area, cm for the lengths.
★Remember
Parallelogram: h = A ÷ b. Triangle: h = A × 2 ÷ b. Then check by multiplying back.
Worked examples
A parallelogram has area 54 m² and base 9 m. Height = 54 ÷ 9 = 6 m. Check: 9 × 6 = 54.
A parallelogram has area 35 cm² and height 5 cm. Base = 35 ÷ 5 = 7 cm.
A triangle has area 30 cm² and base 12 cm. First double the area: 30 × 2 = 60. Then height = 60 ÷ 12 = 5 cm. Check: 12 × 5 ÷ 2 = 30.
Class activity
Which side is missing? Draw three different parallelograms with area 24 cm² on squared paper. Write the base and height of each.
Practice
1
A parallelogram has area 72 cm² and base 12 cm. Find the height.
72 ÷ 12 = 6 cm.
2
A parallelogram has area 48 m² and height 6 m. Find the base.
48 ÷ 6 = 8 m.
3
A triangle has area 40 cm² and height 8 cm. Find the base.
40 × 2 = 80, and 80 ÷ 8 = 10 cm.
4
A triangle has area 27 cm² and base 6 cm. Find the height.
27 × 2 = 54, and 54 ÷ 6 = 9 cm.
5
A parallelogram-shaped field has area 84 m² and base 12 m. Find its height.
84 ÷ 12 = 7 m.