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1 year ago

Find the area of the shape below.

Mathematics

1 answer:

lawyer [7]1 year ago

4 0

9514 1404 393

Answer:

164π cm²

Step-by-step explanation:

The area of a circle is given by the formula ...

A = πr²

The radius (r) is half the diameter (d), so the area of a semicircle in terms of its diameter is ...

1/2A = (1/2)(π)(d/2)² = (π/8)d²

The given shape is the combination of three (3) semicircles. The smallest has a diameter of 6 cm; the middle-sized one has a diameter of (32 cm -6 cm -8 cm) = 18 cm. The largest has a diameter of 32 cm.

The total area will be ...

area of largest + area of middle-size - area of smallest

= (π/8)(32² +18² -6²) = (π/8)(1312) . . . . cm²

The area of the shape is 164π cm².

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