Question

A trapezium is shown below.

Work out the value of x.
If your answer is a decimal, give it to 1 d.p.
x + 4 cm
area = 32 cm²
x + 2 cm
x-1 cm
Not drawn accurately

Answer 1

x = 5

Explanation:

the area (A) of a trapezium is calculated as

A =
`(1)/(2)` h ( b₁ + b₂ )

where h is the perpendicular height between the bases b₁ and b₂

here h = x - 1 , b₁ = x + 2 , b₂ = x + 4 and A = 32

substitute these values into the formula for A

32 =
`(1)/(2)` (x - 1)(x + 2 + x + 4) ← multiply both sides by 2 to clear the fraction

64 = (x - 1)(2x + 6) ← expand product of factors using FOIL

64 = 2X²+ 6x - 2x - 6

64 = 2x² + 4x - 6 ( divide through by 2 )

32 = x² + 2x - 3 ( subtract 32 from both sides )

0 = x² + 2x - 35← quadratic equation in standard form

0 = (x + 7)(x - 5) ← in factored form

equate each factor to zero and solve for x

x + 7 = 0 ⇒ x = - 7

x - 5 = 0 ⇒ x = 5

however, x > 0 , then x = 5