A trapezium has parallel sides of length 22 cm and 10 cm. The non-parallel sides are equal, each of length 13 cm. Find the exact height and area of the trapezium.
Show answer & explanation
Correct answer: C
Explanation
Given:
Parallel sides = 22 cm, 10 cm
Non-parallel sides = 13 cm
According to the formula:
Height of the trapezium = √(Side² − (Difference between bases/2)²)
Area = 1/2 × (a + b) × h
Difference between bases = 22 − 10 = 12
Half the difference = 12/2 = 6
Height
= √(13² − 6²)
= √(169 − 36)
= √133 cm
Area = 1/2 × (22 + 10) × √133
= 1/2 × 32 × √133
= 16√133 cm²
Height = √133 cm
Area = 16√133 cm²