9514 1404 393
Answer:
- area: 524 cm²
- perimeter: 124.8 cm
Step-by-step explanation:
The rectangle in the middle has a width equal to the radius of the semicircular ends, so (20 cm)/2 = 10 cm.
The semicircular ends, together, make a complete circle of radius 10 cm.
The area is the sum of the areas of the parts:
A = LW = (21 cm)(10 cm) = 210 cm² . . . . . . rectangle area
A = πr² = π(10 cm)² = 100π cm² ≈ 314 cm² . . . . . circle area
The total area is ...
210 cm² +314 cm² = 524 cm² . . . . area of the figure
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The perimeter of the figure is the sum of the lengths of all of the edges. From the left, working clockwise, we have ...
P = (1/2 circle of diameter 20) + (rectangle top = 21) +(1/2 circle of diameter 20) +(circle radius = 10) +(rectangle bottom = 21) +(circle radius = 10)
The two 1/2 circles add to a whole circle with a circumference of ...
C = πd = (3.14)(20 cm) = 62.8 cm
Then the whole perimeter is ...
P = 62.8 cm + 21 cm + 10 cm + 21 cm + 10 cm = 124.8 cm
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Note that we have used 3.14 for pi. If you use a more exact value, your answers will be slightly different.
