A trapezium has parallel sides of length 12\text{ cm} and 18\text{ cm}, and a perpendicula… — JAMB UTME

A trapezium has parallel sides of length $12\text{ cm}$ and $18\text{ cm}$ , and a perpendicular height of $7\text{ cm}$ . What is the area of the trapezium?

$105\text{ cm}^2$ Answer
B
$210\text{ cm}^2$
C
$216\text{ cm}^2$
D
$37\text{ cm}^2$

Answer

The area of the trapezium is

105\text{ cm}^2

The area of a trapezium is calculated using the formula

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

, where

a

and

b

are the lengths of the parallel sides, and

h

is the perpendicular height. Substituting

a = 12\text{ cm}

b = 18\text{ cm}

, and

h = 7\text{ cm}

yields

\text{Area} = \frac{1}{2}(12 + 18) \times 7 = \frac{1}{2}(30) \times 7 = 105\text{ cm}^2

Step-by-Step Solution

Identify the given dimensions of the trapezium

Parallel sides

a = 12\text{ cm}

b = 18\text{ cm}

, and height

h = 7\text{ cm}

These are the necessary parameters for the area formula of a trapezium.

Sum the lengths of the parallel sides

a + b = 12 + 18 = 30\text{ cm}

The area formula requires the sum of the bases.

Multiply by the perpendicular height and divide by 2

\text{Area} = \frac{1}{2} \times 30 \times 7 = 15 \times 7 = 105\text{ cm}^2.

Applying the standard formula

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

gives the plane region's total area.

Key Concept

Area of a Trapezium

Question

Answer

Step-by-Step Solution

Key Concept

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