Question

Find the area of the following trapezium:

Answer 1

Given:

Top side (horizontal) = 12 cm

Right vertical side = 4 cm

Slanted side (bottom) = 13 cm

Step-wise calculation:

1. Place coordinates:

Top-left A = (0, 0),

Top-right B = (12, 0),

Right-bottom C = (12, –4). 

Let left-bottom D = (0, –L) so left side AD = L.

2. Distance DC the slanted side = 13 cm: 

`sqrt((12 - 0)^2 + (-4 - (-L))^2) = 13` 

⇒ 144 + (L – 4)² = 169 

⇒ (L – 4)² = 25 

⇒ L – 4 = ±5

⇒ L = 9   ...(Positive)

So, left side AD = 9 cm.

3. The two parallel sides are the vertical sides AD and BC lengths 9 cm and 4 cm; the perpendicular distance between them the “height” for this orientation is 12 cm horizontal separation. 

Use trapezium area formula

A = `1/2` × (Sum of parallel sides) × Distance

A = `1/2 xx (9 + 4) xx 12` 

= `1/2 xx 13 xx 12`

= 78 cm²

4. Perimeter = Sum of all sides

= 12 + 4 + 13 + 9

= 38 cm

Area = 78 cm².

Perimeter = 38 cm.