Question

Find the area and perimeter of the following figure.

Answer 1

Given:

Trapezoid with parallel sides 10 cm (top) and 4 cm (bottom), non‑parallel sides 5 cm and 5 cm.

Rectangle with base 12 cm and diagonal 13 cm. (All lengths in cm.)

Step-wise calculation:

1. Find heights (use Pythagoras).

Trapezoid: horizontal offset of each slanted side

= `(10 - 4)/2`

= 3 cm 

So, trapezoid height

`h_t = sqrt(5^2 - 3^2)` 

= `sqrt(25 - 9)`

= 4 cm

Rectangle: height

`h_r = sqrt(13^2 - 12^2)`

= `sqrt(169 - 144)`

= 5 cm

2. Area (rectangle) = base × height

= 12 × 5

= 60 cm²

Area (trapezoid) = `1/2` × (sum of parallel sides) × height

= `1/2 xx (10 + 4) xx 4`

= 28 cm²

Total area

= 60 + 28

= 88 cm²

3. Perimeter (outline of the combined figure).

Exposed edges: bottom of rectangle = 12.

Right vertical of rectangle = 5.

Right slanted side of trapezoid = 5.

Top of trapezoid = 10.

Left slanted side of trapezoid = 5.

Exposed top of rectangle to the left of trapezoid = 12 – 4 = 8.

Left vertical of rectangle = 5.

Perimeter = 12 + 5 + 5 + 10 + 5 + 8 + 5

= 50 cm

Area = 88 cm².

Perimeter = 50 cm.