Semicircle area calculation worksheet with six problems and formulas.

Explanation:
We are finding the area of semicircles. A semicircle is half of a full circle, so its area is:

\[
\text{Area of semicircle} = \frac{1}{2} \times \pi r^2
\]

Where \( r \) is the radius — half the diameter (the straight line across the bottom of the semicircle).

Let’s go problem by problem.

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1) Diameter = 7 cm → radius \( r = \frac{7}{2} = 3.5 \) cm
Area = \( \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (3.5)^2 = \frac{1}{2} \pi (12.25) = 6.125\pi \)
Now compute numerically:
\( 6.125 \times \pi \approx 6.125 \times 3.1416 \approx 19.242 \)
Rounded to 1 decimal place: 19.2 cm²

(They gave the formula as \( (\pi \times 7^2) \div 2 \), but that’s incorrect — it should be radius squared, not diameter squared. However, looking at the structure, they likely meant \( r = 7 \) cm? Wait — no! The diagram shows 7 cm as the *diameter*, and the formula written says \( (\pi \times r^2) \div 2 \), then substitutes \( r = 7 \). That suggests the 7 cm is being treated as the radius, not diameter.

Let’s double-check: In all diagrams, the measurement shown (e.g., 7 cm, 3 cm, etc.) is the length of the straight edge — that is the diameter. But in problem 1, the formula says “= (π × 7²) ÷ 2”, implying they’re using 7 as radius.

This is a common point of confusion. Let’s look at the diagram style: In standard math worksheets, when a semicircle is drawn with a horizontal line labeled (e.g., “7 cm”), that line is the diameter — because it's the base of the shape.

But the given formula in problem 1 explicitly uses 7 as radius:
A = (π × r²) ÷ 2 = (π × 7²) ÷ 2
So either:
- The label “7 cm” is the radius (unlikely visually), or
- The worksheet expects students to use the given number directly as radius, even if the diagram shows diameter.

However, in problems 3 and 4, the labels are “15 mm” and “8 cm”, and again the formula uses r = that value.

Let’s test with problem 2: diameter labeled 3 cm, formula uses r = 3 → area = (π × 9)/2 ≈ 14.137 → 14.1 cm²
If instead r = 1.5 cm, area = (π × 2.25)/2 ≈ 3.534 → 3.5 cm² — which seems more reasonable for a small semicircle.

But since the worksheet *explicitly writes* “= (π × 7²) ÷ 2”, it’s telling us to treat the given number as the radius, regardless of diagram interpretation.

So we follow the worksheet’s instruction: the number given is the radius.

✔ Confirm with extension problems: #5 has 10 m, #6 has 19 cm — same pattern.

Thus, for all problems, the given length is the radius.

Let’s recalculate accordingly:

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1) r = 7 cm
Area = \( \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (7)^2 = \frac{49\pi}{2} = 24.5\pi \)
24.5 × π ≈ 24.5 × 3.1416 = 76.9692 → 77.0 cm² (to 1 decimal place)

2) r = 3 cm
Area = \( \frac{1}{2} \pi (3)^2 = \frac{9\pi}{2} = 4.5\pi \)
4.5 × 3.1416 = 14.1372 → 14.1 cm²

3) r = 15 mm
Area = \( \frac{1}{2} \pi (15)^2 = \frac{225\pi}{2} = 112.5\pi \)
112.5 × 3.1416 = 353.43 → 353.4 mm²

4) r = 8 cm
Area = \( \frac{1}{2} \pi (8)^2 = \frac{64\pi}{2} = 32\pi \)
32 × 3.1416 = 100.5312 → 100.5 cm²

5) r = 10 m
Area = \( \frac{1}{2} \pi (10)^2 = \frac{100\pi}{2} = 50\pi \)
50 × 3.1416 = 157.08 → 157.1 m²

6) r = 19 cm
Area = \( \frac{1}{2} \pi (19)^2 = \frac{361\pi}{2} = 180.5\pi \)
180.5 × 3.1416 = let’s compute:
180 × 3.1416 = 565.488
0.5 × 3.1416 = 1.5708
Total = 567.0588 → 567.1 cm²

Also, the top blanks:
- Area of a circle = \( \pi r^2 \)
- Area of semicircle = \( \frac{1}{2} \pi r^2 \) or \( \frac{\pi r^2}{2} \)

All answers must include units and be to 1 decimal place.

Final check: Use π ≈ 3.14159265 for precision.

1) 24.5 × π = 76.969 → 77.0
2) 4.5 × π = 14.137 → 14.1
3) 112.5 × π = 353.429 → 353.4
4) 32 × π = 100.531 → 100.5
5) 50 × π = 157.080 → 157.1
6) 180.5 × π = 567.058 → 567.1

All correct.

Final Answer:
Area of a circle = πr²
Area of semicircle = (πr²)/2

1) 77.0 cm²
2) 14.1 cm²
3) 353.4 mm²
4) 100.5 cm²
5) 157.1 m²
6) 567.1 cm²