Mixed practice worksheet for calculating the area of various geometric shapes with given dimensions.

Let’s solve each problem one by one. We’ll use the correct area formulas for each shape and calculate carefully.

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1. Square with side 7 m
Area of square = side × side = 7 × 7 = 49 m²

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2. Rectangle with length 12 ft, width 6 ft
Area of rectangle = length × width = 12 × 6 = 72 ft²

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3. Right triangle with base 8 ft, height 6 ft
Area of triangle = (base × height) ÷ 2 = (8 × 6) ÷ 2 = 48 ÷ 2 = 24 ft²

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4. Circle with diameter 12 m → radius = 6 m
Area of circle = π × r² ≈ 3.14 × 6² = 3.14 × 36 = 113.04 m²

*(We’ll use 3.14 for π unless told otherwise)*

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5. Parallelogram with base 10 ft, height 4 ft
Area of parallelogram = base × height = 10 × 4 = 40 ft²

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6. Trapezoid with bases 3 km and 5 km, height 2 km
Area of trapezoid = ((base1 + base2) × height) ÷ 2 = ((3 + 5) × 2) ÷ 2 = (8 × 2) ÷ 2 = 16 ÷ 2 = 8 km²

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7. Triangle with base 10 cm, height 7 cm
Area = (base × height) ÷ 2 = (10 × 7) ÷ 2 = 70 ÷ 2 = 35 cm²

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8. Circle with diameter 10 ft → radius = 5 ft
Area = π × r² ≈ 3.14 × 5² = 3.14 × 25 = 78.5 ft²

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9. Circle with diameter 7 yd → radius = 3.5 yd
Area = π × r² ≈ 3.14 × (3.5)² = 3.14 × 12.25 = 38.465 yd²
(Rounded to 3 decimal places — or we can leave as is since it’s exact with 3.14)

Actually, let’s compute:
3.5 × 3.5 = 12.25
3.14 × 12.25 =
→ 3 × 12.25 = 36.75
→ 0.14 × 12.25 = 1.715
Total = 36.75 + 1.715 = 38.465 yd²

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10. Shaded part: rectangle minus triangle?
Looking at the figure: It’s a rectangle 6 ft wide and 8 ft tall? Wait — actually, the shaded region is a right triangle on top of a rectangle? No — looking again:

The figure shows a vertical rectangle 6 ft wide, total height 8 ft, but there’s a dashed line from bottom left to top right corner of the rectangle? Actually, no — the shaded region is a quadrilateral that looks like a trapezoid or maybe a triangle plus rectangle?

Wait — re-examining: The figure has a vertical side labeled 8 ft, horizontal bottom 6 ft, and a diagonal dashed line from bottom-left to a point 7 ft up on the right side? Actually, the description says “shaded part” — and the figure is a right trapezoid? Or perhaps it’s a rectangle with a triangle cut out?

Actually, looking closely: The shaded region is a polygon with vertices at bottom-left, bottom-right, then up 7 ft on the right, then diagonally to top-left? That would make it a trapezoid with parallel sides 8 ft and 7 ft? No.

Wait — better interpretation: The entire figure is a rectangle 6 ft wide and 8 ft high. There’s a dashed line from bottom-left corner to a point 7 ft up on the right side. The shaded region is the part BELOW that diagonal? So it’s a triangle? But that doesn’t match.

Alternatively — the shaded region is a right triangle with legs 6 ft and 7 ft? Because the dashed line goes from bottom-left to a point 7 ft up on the right edge, and the bottom is 6 ft. So if you connect those, the shaded region might be the triangle formed by bottom-left, bottom-right, and the point 7 ft up on the right? That would be a right triangle with base 6 ft and height 7 ft.

Yes — that makes sense. So area = (6 × 7) ÷ 2 = 42 ÷ 2 = 21 ft²

But wait — the full height is 8 ft, and the point is at 7 ft — so maybe the unshaded part is a small triangle on top? Let me think differently.

Actually, standard interpretation for such figures: The shaded region is a trapezoid with parallel sides 7 ft and 8 ft, and width 6 ft? No — because the non-parallel sides are not both vertical.

Better approach: The figure is a rectangle 6 ft by 8 ft. A diagonal is drawn from bottom-left to a point 7 ft up on the right side. The shaded region is the quadrilateral below that line? Then it’s a trapezoid with bases 7 ft and 8 ft? No.

Actually, let's consider coordinates:

Place bottom-left at (0,0), bottom-right at (6,0), top-right at (6,8), top-left at (0,8). The dashed line goes from (0,0) to (6,7). The shaded region is the polygon bounded by (0,0), (6,0), (6,7), and back to (0,0)? That would be a triangle? No — from (0,0) to (6,0) to (6,7) to (0,0) — that’s a right triangle with legs 6 and 7? But then why is the full height 8 mentioned?

Perhaps the shaded region is the area under the line from (0,0) to (6,7), which is a triangle with base 6 and height 7 — area = (6×7)/2 = 21 ft².

I think that’s it. So 21 ft²

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11. Triangle with base 16 m, height 20 m
Area = (base × height) ÷ 2 = (16 × 20) ÷ 2 = 320 ÷ 2 = 160 m²

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12. Parallelogram with base 12 ft, height 4 ft
Area = base × height = 12 × 4 = 48 ft²

Note: The 10 ft is the slant side — we don’t use that for area; only base and perpendicular height.

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Now, let’s list all answers clearly:

1. 49 m²
2. 72 ft²
3. 24 ft²
4. 113.04 m²
5. 40 ft²
6. 8 km²
7. 35 cm²
8. 78.5 ft²
9. 38.465 yd²
10. 21 ft²
11. 160 m²
12. 48 ft²

Double-checking #10: If the figure is a rectangle 6x8, and a line from bottom-left to (6,7), and shaded is the triangle below — yes, base 6, height 7 → area 21. Correct.

#9: 3.14 * 3.5^2 = 3.14 * 12.25 = let's recalculate:
12.25 * 3 = 36.75
12.25 * 0.14 = 12.25 * 0.1 = 1.225; 12.25 * 0.04 = 0.49; total 1.225+0.49=1.715
36.75 + 1.715 = 38.465 — correct.

All others seem straightforward.

Final Answer:
1. 49 m²
2. 72 ft²
3. 24 ft²
4. 113.04 m²
5. 40 ft²
6. 8 km²
7. 35 cm²
8. 78.5 ft²
9. 38.465 yd²
10. 21 ft²
11. 160 m²
12. 48 ft²