To solve the
Area of Trapezoid Worksheet, we use the standard formula for the area of a trapezoid:
>
Area = ½ × (Base₁ + Base₂) × Height
Where:
-
Base₁ and
Base₂ are the lengths of the two parallel sides (the top and bottom bases).
-
Height is the perpendicular distance between the two bases (marked with a right-angle symbol in each diagram).
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Let’s solve each problem one by one.
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Problem 1
- Bases: 15 mi and 10 mi
- Height: 13 mi
Area = ½ × (15 + 10) × 13 = ½ × 25 × 13 = 12.5 × 13 = 162.5 mi²
✔ Answer: 162.5 square miles
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Problem 2
- Bases: 20 ft and 30 ft
- Height: 10.5 ft
Area = ½ × (20 + 30) × 10.5 = ½ × 50 × 10.5 = 25 × 10.5 = 262.5 ft²
✔ Answer: 262.5 square feet
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Problem 3
- Bases: 10 in and 16 in
- Height: 7 in
Area = ½ × (10 + 16) × 7 = ½ × 26 × 7 = 13 × 7 = 91 in²
✔ Answer: 91 square inches
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Problem 4
- Bases: 9 km and 18.5 km
- Height: 5.8 km
Area = ½ × (9 + 18.5) × 5.8 = ½ × 27.5 × 5.8 = 13.75 × 5.8
Let’s compute:
13.75 × 5.8
= 13.75 × (5 + 0.8)
= (13.75 × 5) + (13.75 × 0.8)
= 68.75 + 11
=
79.75 km²
✔ Answer: 79.75 square kilometers
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Problem 5
- Bases: 22.7 cm and 5.3 cm
- Height: 6.9 cm
Area = ½ × (22.7 + 5.3) × 6.9 = ½ × 28 × 6.9 = 14 × 6.9
Compute:
14 × 6.9 = 14 × (7 - 0.1) = 98 - 1.4 =
96.6 cm²
✔ Answer: 96.6 square centimeters
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Problem 6
- Bases: 5.8 yd and 13.8 yd
- Height: 4 yd
Area = ½ × (5.8 + 13.8) × 4 = ½ × 19.6 × 4 = 9.8 × 4 = 39.2 yd²
✔ Answer: 39.2 square yards
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Problem 7
- Bases: 4.5 in and 12.8 in
- Height: 9 in
Area = ½ × (4.5 + 12.8) × 9 = ½ × 17.3 × 9 = 8.65 × 9
Compute:
8.65 × 9 = (8 × 9) + (0.65 × 9) = 72 + 5.85 =
77.85 in²
✔ Answer: 77.85 square inches
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Problem 8
- Bases: 11 km and 1.8 km
- Height: 6.4 km
Area = ½ × (11 + 1.8) × 6.4 = ½ × 12.8 × 6.4 = 6.4 × 6.4
Wait — ½ × 12.8 = 6.4, so yes:
6.4 × 6.4 = 40.96 km²
✔ Answer: 40.96 square kilometers
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##
✔ Final Answers:
1.
162.5 mi²
2.
262.5 ft²
3.
91 in²
4.
79.75 km²
5.
96.6 cm²
6.
39.2 yd²
7.
77.85 in²
8.
40.96 km²
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💡
Tip: Always double-check that you’re using the
two parallel sides as bases and the
perpendicular height — not the slanted side! The right-angle symbol tells you which dimension is the height.
Let me know if you’d like to see any step visualized or explained further!
Parent Tip: Review the logic above to help your child master the concept of area of a trapezoid worksheet.
