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Complete the Area Formulas
publish date: 2026/05/17 19:43:29.043967 UTC
Drag the correct expression into each placeholder.
Full circle area: \(A = \pi\) × (1)
Semicircle area: \(A = \) (2) \(\times \pi r^2\)
In the 6–8–10 composite figure:
Triangle area = ½ × 6 × 8 = (3) in²
Smaller semicircle (\(r=4\)) area = (4) \(\pi\) in²
Larger semicircle (\(r=5\)) area = (5) \(\pi\) in²
Please drag and drop the selected option in the right place or type it instead
r²
½
24
8
12.5
Correct Answer
(1) r²
(2) ½
(3) 24
(4) 8
(5) 12.5
Explanation
Full circle: \(A = \pi r^2\) — square the radius, then multiply by \(\pi\).
Semicircle: \(A = \frac{1}{2}\pi r^2\) — half of the full circle area.
Components of the 6–8–10 composite:
- Triangle: \(\frac{1}{2}(6)(8) = 24\) in²
- Smaller semicircle (\(r=4\)): \(\frac{1}{2}\pi(4)^2 = \frac{1}{2}\pi(16) = 8\pi\) in²
- Larger semicircle (\(r=5\)): \(\frac{1}{2}\pi(5)^2 = \frac{1}{2}\pi(25) = 12.5\pi\) in²
- Total: \(24 + 8\pi + 12.5\pi \approx 88.40\) in²
Reference
Mathematics for college students