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Area of triangles, parallelograms and trapezoids
Dynamic tasks on finding areas, bases and heights of triangles, parallelograms and trapezoids.
Questions: 10Estimated time: 20 minutes
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Question 1out of 10
A triangle and a parallelogram each have base 9 cm and height 5 cm. Compare their areas.
With the same base and height, the parallelogram area is a × h and the triangle area is a × h ÷ 2. The parallelogram area is twice the triangle area.
Question 2out of 10
A trapezoid has bases 10 cm and 20 cm and area 150 cm². Find its height.
Rearranging trapezoid area S = (a + b) × h ÷ 2 gives h = 2 × S ÷ (a + b). Double the area and divide by the sum of the bases.
Question 3out of 10
A parallelogram has area 153 cm² and height 9 cm. Find its base length.
Parallelogram area is S = base × height, so base = S ÷ h. Divide the area by the given height. The result is a length in centimetres.
Question 4out of 10
A parallelogram has base 13 cm and height 10 cm. Calculate its area.
Parallelogram area is S = base × perpendicular height. Multiply a by h; a sloping side is not the height unless it is perpendicular to the base.
Question 5out of 10
A triangle has area 56 cm² and base 16 cm. Find the corresponding height.
From S = a × h ÷ 2, obtain h = 2 × S ÷ a. Double the area and divide by the base length. Express the height in cm.
Question 6out of 10
What does the height mean in the trapezoid area formula?
A trapezoid height is the perpendicular distance between its parallel bases. A sloping leg is generally longer and cannot replace the height in the area formula.
Question 7out of 10
A parallelogram has area 70 cm² and height 7 cm. Find its base length.
Parallelogram area is S = base × height, so base = S ÷ h. Divide the area by the given height. The result is a length in centimetres.
Question 8out of 10
A trapezoid has bases 9 cm and 15 cm and height 4 cm. Calculate its area.
Trapezoid area is S = (a + b) × h ÷ 2. Add the two parallel bases, multiply by the perpendicular height and divide by 2.
Question 9out of 10
A triangle has base 10 cm and corresponding height 9 cm. Calculate its area.
Triangle area is S = base × perpendicular height ÷ 2. Multiply the given lengths, then divide by 2. Use cm².
Question 10out of 10
Triangle ABC has AB = AC. M is the midpoint of BC and G is the intersection of the triangle medians. GM = 4 cm and triangle ABG has area 36 cm². Find the length of BC. The drawing is not to scale.
The median to the base of an isosceles triangle is also an altitude. The intersection of the medians divides each median in the ratio 2 : 1 from the vertex: use GM to find AG. For triangle ABG with AG as the base, the corresponding height is BM. Use the area formula to find BM, then use the fact that M is the midpoint of BC.
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Sample questions
- A triangle has base ___ cm and corresponding height ___ cm. Calculate its area.
- A triangle has area ___ cm² and base ___ cm. Find the corresponding height.
- A parallelogram has base ___ cm and height ___ cm. Calculate its area.
- A parallelogram has area ___ cm² and height ___ cm. Find its base length.
- A trapezoid has bases ___ cm and ___ cm and height ___ cm. Calculate its area.
Area of triangles, parallelograms and trapezoids
A triangle has A = ah/2, a parallelogram A = ah and a trapezoid A = (a + b)h/2. The height must be perpendicular to the selected base.
Unknown dimensions
Rearrange the formula to find a base or height from a known area. In a trapezoid, a and b are the parallel sides only. Convert units before calculating and express area in square units.
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