The design decides
Show on a big screenThe same pieces give two different totals.
- Same square, same semicircle, radius 7.
- Bed: the semicircle sticks out.
- Pond: the same semicircle is cut in.
The rule
A square courtyard of side 14 covers 196. A bed is a patch for flowers. A semicircular bed of radius 7 is built on one side. It sticks out of the courtyard. The full circle of radius 7 has area 154. So the bed covers 77.
Bed = 196 + 77 = 273.
The same semicircle is dug into the courtyard as a pond. It is cut into the courtyard instead.
Pond = 196 − 77 = 119.
Add the round piece when it sticks out of the shape. Subtract it when it is cut out of the shape.
The two totals differ by 273 − 119 = 154. That equals 77 + 77, the area of the whole circle. The pieces stay the same. Only their place in the design changes.
Slide the square. Tap bed or pond. Watch the sign.
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Try the lab to finish this lesson.