Area Formulas for Plane Figures

Imagine a landscape designer estimating materials for three sections of a park. She uses area formulas to find how much space each section covers.

She begins with a rectangular lawn measuring 18 meters long by 12 meters wide. She uses the formula for the area of a rectangle, which is length times width.

By multiplying 18 by 12, she finds that the lawn covers 216 square meters.

Next, she plans a circular flower bed with a radius of 3 meters. She applies the formula for the area of a circle, which is pi times the radius squared.

She substitutes 3 meters for the radius. Squaring 3 gives 9, so the area is pi times 9, or approximately 28.27 square meters, helping determine the soil needed.

Finally, she designs a triangular picnic area with a 9-meter base and a 6-meter height. She uses the formula for the area of a triangle, which is half the base times the height.

She calculates that the picnic area covers 27 square meters, showing how much paving material is needed.

The designer uses these formulas to determine the materials needed, helping her purchase the right amounts without under- or overestimating.