Question

The area of ΔABC = 18 cm². Find the distance between the || lines AD and BC if BC = 8 cm. Calculate the area of || gm BCDE.

Answer 1

Given:

• ΔABC with area = 18 cm²
• BC = 8 cm
• AD || BC (so AD and BC are parallel lines, presumably forming a parallelogram BCDE with BC as one side)

Find:

• Distance between parallel lines AD and BC
• Area of parallelogram BCDE

Step 1: Recall area formula of a triangle

Area(ΔABC) = `1/2` × base × height

Take BC as base, height = Distance from A to BC = h

`18 = 1/2 xx 8 xx h`

`18 = 4 xx h`

`h = 18/4`

= 4.5 cm

So the distance between parallel lines AD and BC = 4.5 cm

Step 2: Area of parallelogram BCDE

Parallelogram BCDE has base = BC = 8 cm and height = distance between parallel lines = 4.5 cm

Area(BCDE) = base × height

= 8 × 4.5

= 36 cm²