Area of Trapezoids Worksheets - Free Printable

To find the area of a trapezoid, we use this formula:

Area = (Base 1 + Base 2) × Height ÷ 2

Or written another way:
Area = ½ × (b₁ + b₂) × h

Let’s solve each problem one by one. I’ll show my work for each so you can follow along.

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Problem 1:
Bases: 6 in and 4 in
Height: 3 in
→ Area = ½ × (6 + 4) × 3 = ½ × 10 × 3 = 5 × 3 = 15 in²

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Problem 2:
Bases: 8 ft and 5 ft
Height: 4 ft
→ Area = ½ × (8 + 5) × 4 = ½ × 13 × 4 = 6.5 × 4 = 26 ft²

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Problem 3:
Bases: 9 yd and 7 yd
Height: 5 yd
→ Area = ½ × (9 + 7) × 5 = ½ × 16 × 5 = 8 × 5 = 40 yd²

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Problem 4:
This is a triangle? Wait — no, looking at the shape, it's actually a trapezoid with bases 3 m and 5 m, height 4 m.
But wait — the diagram shows two parallel sides: top = 3 m, bottom = 5 m, height = 4 m (vertical distance between them).
→ Area = ½ × (3 + 5) × 4 = ½ × 8 × 4 = 4 × 4 = 16 m²

*(Note: Even though it looks tilted, as long as we have the perpendicular height and the two parallel bases, the formula works.)*

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Problem 5:
Bases: 7 m and 5 m
Height: 6 m
→ Area = ½ × (7 + 5) × 6 = ½ × 12 × 6 = 6 × 6 = 36 m²

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Problem 6:
Bases: 8 ft and 5 ft
Height: 4 ft
→ Area = ½ × (8 + 5) × 4 = ½ × 13 × 4 = 6.5 × 4 = 26 ft²

*(Same as Problem 2 — different units but same numbers.)*

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Problem 7:
Bases: 10 cm and 6 cm
Height: 5 cm
→ Area = ½ × (10 + 6) × 5 = ½ × 16 × 5 = 8 × 5 = 40 cm²

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Problem 8:
This one has a rectangle part and a triangle? Actually, it’s a trapezoid split into a rectangle and a right triangle. But we don’t need to split it — just use the trapezoid formula.

Top base = 10 yd
Bottom base = 10 yd + 4 yd = 14 yd? Wait — let me check.

Actually, looking carefully: The figure shows a trapezoid where the top base is 10 yd, the bottom base is longer because there’s a 4 yd extension on the side. So bottom base = 10 + 4 = 14 yd? No — that’s not correct.

Wait — actually, in trapezoid problems like this, if they give you the “overhang” or extra length, you add it to get the full bottom base.

Looking again: The vertical side is 6 yd (height), top base is 10 yd, and the slanted side adds 4 yd horizontally to the bottom. So yes — bottom base = 10 + 4 = 14 yd.

→ Area = ½ × (10 + 14) × 6 = ½ × 24 × 6 = 12 × 6 = 72 yd²

*(Alternatively, you could think of it as a rectangle 10×6 plus a triangle with base 4 and height 6: area = 60 + 12 = 72 — same answer.)*

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Problem 9:
Bases: 8 in and 4 in
Height: 5 in
→ Area = ½ × (8 + 4) × 5 = ½ × 12 × 5 = 6 × 5 = 30 in²

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Now let’s double-check all answers quickly:

1. ½*(6+4)*3 = 15 ✔
2. ½*(8+5)*4 = 26 ✔
3. ½*(9+7)*5 = 40 ✔
4. ½*(3+5)*4 = 16 ✔
5. ½*(7+5)*6 = 36 ✔
6. ½*(8+5)*4 = 26 ✔
7. ½*(10+6)*5 = 40 ✔
8. ½*(10+14)*6 = 72 ✔
9. ½*(8+4)*5 = 30 ✔

All calculations are correct.

Final Answer:
1. 15 in²
2. 26 ft²
3. 40 yd²
4. 16 m²
5. 36 m²
6. 26 ft²
7. 40 cm²
8. 72 yd²
9. 30 in²