Why Area Matters

Area is the amount of two-dimensional space a shape covers. Whether you're tiling a floor, painting a wall, or designing a garden, you need to calculate area.

In this section we move beyond rectangles and triangles to explore some more interesting quadrilaterals — trapeziums, parallelograms, rhombuses, and kites — and then combine shapes to tackle compound (composite) shapes.

Area

The measure of the two-dimensional space enclosed by a shape, expressed in square units (e.g. cm², m², km²).

Exam Tip

Always check which measurements you've been given before choosing a formula. The key measurements are usually a base and a height (perpendicular height, not a slanted side).

Area of a Parallelogram

A parallelogram is a quadrilateral with two pairs of parallel sides. Think of it as a rectangle that has been "pushed over" — a slanted rectangle.

Parallelogram

A quadrilateral where both pairs of opposite sides are parallel and equal in length.

The formula for the area of a parallelogram is:

$A = b \times h$

where

$b$ = the length of the base
$h$ = the perpendicular height (the vertical distance between the base and the opposite side)

Analogy

Imagine cutting a right-angled triangle off one end of the parallelogram and sliding it to the other end. You'd get a perfect rectangle! That's why the formula is the same as for a rectangle: $base \times height$ .

Warning

The height must be perpendicular (at 90°) to the base. Do not use the slant side length as the height — this is one of the most common mistakes students make.

Example

Find the area of a parallelogram with base 12 cm and perpendicular height 7 cm.

Step 1: Write the formula: $A = b \times h$

Step 2: Substitute: $A = 12 \times 7$

Step 3: Calculate: $A = 84 cm^{2}$

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