To find the area of a trapezoid, we use this formula:
Area = ½ × (Base₁ + Base₂) × Height
That means:
- Add the two parallel sides (the bases).
- Multiply that sum by the height (the perpendicular distance between the bases).
- Then divide by 2 (or multiply by ½).
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
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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
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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
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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
First, 27.5 × 5.8:
Break it down:
27.5 × 5 = 137.5
27.5 × 0.8 = 22
Total = 137.5 + 22 = 159.5
Then half of that: 159.5 ÷ 2 =
79.75 km²
Wait — let me recalculate carefully:
Actually, better to do:
½ × 27.5 = 13.75
Then 13.75 × 5.8
Compute 13.75 × 5.8:
13.75 × 5 = 68.75
13.75 × 0.8 = 11
Total = 68.75 + 11 =
79.75 km² ✔
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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
14 × 6 = 84
14 × 0.9 = 12.6
Total = 84 + 12.6 =
96.6 cm²
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Problem 6:
Bases: 5.8 yd and 13.8 yd
Height: 4 yd
(Note: The side labeled 6.2 yd is not needed — it’s a slant side, not the height.)
Area = ½ × (5.8 + 13.8) × 4
= ½ × 19.6 × 4
= 9.8 × 4
=
39.2 yd²
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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
8 × 9 = 72
0.65 × 9 = 5.85
Total = 72 + 5.85 =
77.85 in²
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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
=
40.96 km²
(Yes! 6.4 squared is 40.96 — nice coincidence!)
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Final Answer:
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
Parent Tip: Review the logic above to help your child master the concept of quadrilateral area worksheet answers.
