Question

Find the perimeter of the following trapezium:

Answer 1

Given:

Top base = 30 m.

Vertical height = 12 m (distance between bases).

Horizontal offsets at each bottom corner = 5 m (so bottom base = 30 + 5 + 5).

Slanted sides are equal (isosceles trapezium).

Step-wise calculation:

1. Bottom base

= 30 + 5 + 5

= 40 m

2. Each slanted side length

= `sqrt("height"^2 + "offset"^2)`

= `sqrt(12^2 + 5^2)`

= `sqrt(144 + 25)`

= `sqrt(169)`

= 13 m

3. Area using A = `1/2` × (sum of parallel sides) × height:

A = `1/2 xx (30 + 40) xx 12`

= `1/2 xx 70 xx 12`

= 35 × 12

= 420 m²

4. Perimeter

= 30 + 40 + 13 + 13 

= 96 m

Area = 420 m².

Perimeter = 96 m.