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How to find the area of a stadium-shaped field

A rectangle plus one circle in area

If a semicircle is attached to each short side of an $L$ by $W$ rectangle, their diameters are both $W$ . Together the semicircles have the area of a full circle with radius $W /2$ , so $A = L W + π (W /2)^{2}$ .

Problem

A field is formed by joining an $85$ m by $52$ m rectangle and two semicircles, one on each $52$ m side. Find the total area using $π = 3.14$ .

Answer

6, 542.64 m^{2}

The semicircles are outside the rectangle and do not overlap it.

Step-by-step solution

1. Find the rectangular part

A_{rect} = 85 \cdot 52 = 4420 m^{2} .

2. Treat the two ends as a circle

Each semicircle has diameter $52$ m and radius $26$ m. Together they contribute

A_{ends} = 3.14 \cdot 2 6^{2} = 2122.64 m^{2} .

3. Add the non-overlapping areas

A_{field} = 4420 + 2122.64 = 6542.64 m^{2} .

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