A trapezium has parallel sides of lengths 8\text{ cm} and 12\text{ cm}. If the perpendicul… — JAMB UTME

A trapezium has parallel sides of lengths $8\text{ cm}$ and $12\text{ cm}$ . If the perpendicular distance between these parallel sides is $6\text{ cm}$ , what is the area of the trapezium?

$60\text{ cm}^2$ Answer
B
$120\text{ cm}^2$
C
$10\text{ cm}^2$
D
$288\text{ cm}^2$

Answer

60\text{ cm}^2

The area of a trapezium is given by

A = \frac{1}{2}(a + b)h

, where

a

and

b

are the parallel sides and

h

is the perpendicular distance between them. Substituting

a = 8

b = 12

, and

h = 6

gives

A = \frac{1}{2}(8 + 12)(6) = \frac{1}{2}(20)(6) = 60\text{ cm}^2

Step-by-Step Solution

Identify the given dimensions and the formula for the area of a trapezium.

Parallel sides

a = 8\text{ cm}

b = 12\text{ cm}

, height

h = 6\text{ cm}

. Formula:

A = \frac{1}{2}(a + b)h

The area of a trapezium depends on the sum of its parallel sides and its perpendicular height.

Sum the parallel sides.

a + b = 8 + 12 = 20\text{ cm}

The average of the parallel sides forms the effective width of an equivalent rectangle.

Multiply by half of the height to find the total area.

A = \frac{1}{2} \times 20 \times 6 = 60\text{ cm}^2

Completing the formula gives the exact plane surface measure in square centimeters.

Key Concept

Area of a Trapezium

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