An isosceles trapezium has parallel sides of lengths 14\text{ cm} and 8\text{ cm}. If each… — JAMB UTME

An isosceles trapezium has parallel sides of lengths $14\text{ cm}$ and $8\text{ cm}$ . If each of the non-parallel sides has a length of $5\text{ cm}$ , calculate the area of the trapezium in $\text{cm}^2$ .

Answer: 44 cm²

Answer

The area of the trapezium is

44\text{ cm}^2

Projecting the top base of length

8\text{ cm}

onto the bottom base of length

14\text{ cm}

leaves a difference of

6\text{ cm}

, which is divided equally into two

3\text{ cm}

segments on either side. Using the Pythagorean theorem with the non-parallel side (

5\text{ cm}

) and the base segment (

3\text{ cm}

) gives a height of

4\text{ cm}

. The area is then calculated as

\frac{1}{2} \times (14 + 8) \times 4 = 44\text{ cm}^2

Step-by-Step Solution

Determine the projection segment length on the longer base

x = \frac{14 - 8}{2} = 3\text{ cm}

Since the trapezium is isosceles, dropping perpendiculars from both ends of the top base creates two identical right-angled triangles at the sides.

Calculate the perpendicular height using the Pythagorean theorem

h = \sqrt{5^2 - 3^2} = \sqrt{16} = 4\text{ cm}

The slant side (

5\text{ cm}

), the height (

h

), and the projection segment (

3\text{ cm}

) form a right-angled triangle.

Calculate the area of the trapezium

\text{Area} = \frac{1}{2}(14 + 8) \times 4 = 44\text{ cm}^2

The area of a trapezium is given by half the sum of its parallel sides multiplied by its perpendicular height.

Key Concept

Perimeter and Area of Plane Shapes - Area of Isosceles Trapezium

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