Area of special quadrilaterals
Find the area of parallelograms using , trapeziums using , and rhombuses and kites using .
Worked examples
Finding the area of a parallelogram
Straightforward
Problem
Find the area of a parallelogram with base cm and perpendicular height cm.
1
Write the formula for the area of a parallelogram.
2
Substitute and .
3
Calculate the area.
cm²
Answer
cm²
Finding the area of a trapezium
Moderate
Problem
Find the area of a trapezium with parallel sides cm and cm, and perpendicular height cm.
1
Write the formula for the area of a trapezium.
2
Substitute , and .
3
Add the parallel sides.
4
Calculate the area.
cm²
Answer
cm²
Finding a missing diagonal of a rhombus
Challenging
Problem
A rhombus has area cm² and one diagonal of length cm. Find the length of the other diagonal.
1
Write the formula for the area of a rhombus.
2
Substitute and .
3
Multiply both sides by .
4
Divide both sides by .
cm
Answer
cm
Practise
Q1·Straightforward
Find the area of a parallelogram with base cm and perpendicular height cm.
Explanation
cm²
Q2·Straightforward
Find the area of a parallelogram with base m and perpendicular height m.
Explanation
m²
Q3·Straightforward
A parallelogram has base cm and perpendicular height cm. Find its area.
Explanation
cm²
Q4·Straightforward
Find the area of a parallelogram with base m and perpendicular height m.
Explanation
m²
Q5·Moderate
Find the area of a trapezium with parallel sides cm and cm, and perpendicular height cm.
Explanation
cm²
Q6·Moderate
A trapezium has parallel sides of m and m, and a perpendicular height of m. Find its area.
Explanation
m²
Q7·Moderate
Find the area of a trapezium with parallel sides cm and cm, and perpendicular height cm.
Explanation
cm²
Q8·Moderate
A trapezium has area cm². One parallel side is cm and the perpendicular height is cm. Find the length of the other parallel side.
Explanation
cm
Q9·Challenging
Find the area of a rhombus with diagonals cm and cm.
Explanation
cm²
Q10·Challenging
A kite has diagonals of length cm and cm. Find its area.
Explanation
cm²
Q11·Challenging
A rhombus has area cm² and one diagonal of length cm. Find the length of the other diagonal.
Explanation
cm
Q12·Challenging
A kite has area cm² and one diagonal of length cm. Find the length of the other diagonal.
Explanation
cm