10E

Area of parallelograms and composite figures

The area of a parallelogram, and finding the area of composite shapes by adding or subtracting simpler shapes.

Parallelograms

Parallelogram

$$A = bh$$

Example 1●●

An L shape is a $10$ m by $8$ m rectangle with a $6$ m by $5$ m rectangle cut from one corner. Find its area.

$10 \times 8 = 80$ m²

$80 - 6 \times 5 = 80 - 30 = 50$ m²

Example 2●●

A house shape is a $6$ m by $4$ m rectangle with a triangle of base $6$ m and height $3$ m on top. Find its area.

$6 \times 4 + \tfrac{1}{2} \times 6 \times 3 = 24 + 9 = 33$ m²

Flashcards

Area of a parallelogram

$A = bh$ (perpendicular height)

Composite area

Add the parts, or subtract the hole.

Parallelogram base 9, height 4

$36$

Practice

Find the area of the L shape in Example 1 (m²).
Find the area of the house shape in Example 2 (m²).
A parallelogram has base $9$ cm and height $4$ cm. Find its area.
A parallelogram has base $8$ cm, slant side $6$ cm and height $5$ cm. Find its area.
A $10$ cm square has a $4$ cm square hole. Find the remaining area.
A parallelogram has area $48$ m² and base $8$ m. Find its height.
A $4$ by $4$ square sits next to a $2$ by $3$ rectangle. Find the total area.
A path $1$ m wide goes around a $6$ m by $10$ m lawn. Find the area of the path (m²).