Explanation:
We are finding the area of trapezoids. The formula for the area of a trapezoid is:
Area = (base₁ + base₂) × height ÷ 2
Where:
- base₁ and base₂ are the lengths of the two parallel sides (the top and bottom),
- height is the perpendicular distance between them (shown with a right-angle mark).
Let’s solve each one step by step.
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1. Top = 15 mi, Bottom = 10 mi, Height = 13 mi
Area = (15 + 10) × 13 ÷ 2 = 25 × 13 ÷ 2 = 325 ÷ 2 =
162.5 mi²
✔ Check: 25 × 13 = 325 → half is 162.5 ✔️
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2. Top = 20 ft, Bottom = 30 ft, Height = 10.5 ft
Area = (20 + 30) × 10.5 ÷ 2 = 50 × 10.5 ÷ 2 = 525 ÷ 2 =
262.5 ft²
✔ 50 × 10.5 = 525 → half is 262.5 ✔️
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3. Top = 10 in, Bottom = 16 in, Height = 7 in
Area = (10 + 16) × 7 ÷ 2 = 26 × 7 ÷ 2 = 182 ÷ 2 =
91 in²
✔ 26 × 7 = 182 → half is 91 ✔️
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4. Top = 9 km, Bottom = 18.5 km, Height = 5.8 km
Area = (9 + 18.5) × 5.8 ÷ 2 = 27.5 × 5.8 ÷ 2
First: 27.5 × 5.8
Break it down:
27.5 × 5 = 137.5
27.5 × 0.8 = 22
So total = 137.5 + 22 = 159.5
Now divide by 2: 159.5 ÷ 2 =
79.75 km²
✔ Double-check: 27.5 × 5.8 = (55/2) × (58/10) = (55×58)/(20) = 3190/20 = 159.5 → ÷2 = 79.75 ✔️
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5. This one is tricky — the height is labeled 6.9 cm, but look carefully: the right angle is between the side of length 6.9 cm and the base of 5.3 cm. However, the height must be perpendicular to *both* bases. In this diagram, the height is actually the vertical segment shown with the right angle — that’s 6.9 cm, and the two parallel sides are 22.7 cm (top) and 5.3 cm (bottom). Yes — the slanted side is 7.9 cm, but we don’t need that.
So:
Top = 22.7 cm, Bottom = 5.3 cm, Height = 6.9 cm
Area = (22.7 + 5.3) × 6.9 ÷ 2 = 28 × 6.9 ÷ 2
28 × 6.9 = 28 × (7 − 0.1) = 196 − 2.8 = 193.2
Then ÷2 =
96.6 cm²
✔ Alternative: 28 × 6.9 = (20×6.9)+(8×6.9)=138+55.2=193.2 → ÷2 = 96.6 ✔️
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6. Top = 5.8 yd, Bottom = 13.8 yd, Height = 4 yd
Area = (5.8 + 13.8) × 4 ÷ 2 = 19.6 × 4 ÷ 2 = 78.4 ÷ 2 =
39.2 yd²
✔ 19.6 × 4 = 78.4 → half = 39.2 ✔️
Note: The 6.2 yd side is slanted — not needed.
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7. Top = 4.5 in, Bottom = 12.8 in, Height = 9 in
Area = (4.5 + 12.8) × 9 ÷ 2 = 17.3 × 9 ÷ 2
17.3 × 9 = (17 × 9) + (0.3 × 9) = 153 + 2.7 = 155.7
÷2 =
77.85 in²
✔ Verified ✔️
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8. Top = 11 km, Bottom = 1.8 km, Height = 6.4 km
Area = (11 + 1.8) × 6.4 ÷ 2 = 12.8 × 6.4 ÷ 2
First: 12.8 × 6.4
Think: 128 × 64 = 8192, then divide by 100 (since 12.8 = 128/10, 6.4 = 64/10 → product = 8192/100 = 81.92)
So 12.8 × 6.4 = 81.92
Now ÷2 =
40.96 km²
✔ Double-check: 12.8 × 6 = 76.8; 12.8 × 0.4 = 5.12; sum = 81.92 → ÷2 = 40.96 ✔️
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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 trapezoid area worksheet.
