Reading a design into pieces
Show on a big screenA medal card has no formula of its own. It is a rectangle with a rounded end.
- One shape: rectangle with a rounded end.
- Split into two known pieces.
- Rectangle: 20 × 14 = 280.
- Semicircle: half of 154 = 77.
- Total = 280 + 77 = 357.
The rule
A shape with no formula splits into pieces that do.
Name each round piece's share of the turn. Compute it. Then add or subtract it.
A medal card is a 20-by-14 rectangle plus a semicircle. A semicircle is half a circle. Its radius is 7, and it sits on one 14 side. That makes the rounded end.
Rectangle = 20 × 14 = 280. The full circle of radius 7 has area 154. Semicircle = half of 154 = 77. Card = 280 + 77 = 357 square units.
Check the piece against the picture each time.
Watch out!
The card is 14 wide. That width is the semicircle's diameter, not its radius. A diameter is the full width across a circle. Radius = 14 ÷ 2 = 7.
Drag the half circle onto a 14 side of the card. Slide the length. Read the total.
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Try the lab to finish this lesson.