Question

The lengths of the adjacent sides of a plot of land in the form of a parallelogram are 15 m and 13 m. If a diagonal is 14 m, find its area.

Answer 1

Given: The adjacent sides are 15 m and 13 m and a diagonal is 14 m.

Step-wise calculation:

1. Let the diagonal split the parallelogram into two congruent triangles with sides 15 m, 13 m and 14 m.

2. Compute the semi-perimeter of one triangle:

`s = (15 + 13 + 14)/2`

= `42/2`

= 21

3. Use Heron’s formula for the triangle’s area:

Area_triangle = `sqrt(s(s - 15)(s - 13)(s - 14)`

= `sqrt(21 xx 6 xx 8 xx 7)`

= `sqrt(7056)`

= 84 m²

4. The parallelogram consists of two such congruent triangles.

So, `"area"_"parallelogram" = 2 xx "area"_"triangle"`

= 2 × 84

= 168 m²

The area of the parallelogram is 168 m².