Area of a Trapezoid Worksheet: Grade 7
Focus: Rearranging algebraic formulas, solving for unknown height h or missing base b.
The area of a trapezium is 34 cm². The length of one of the parallel sides is 10 cm and its height is unknown. If the other parallel side is 4 cm, find the height. (Classic NCERT Class 8 / Grade 7 problem)
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34 = ½ × (10 + 4) × h
34 = ½ × 14 × h = 7h
h = 34 / 7 ≈ 4.86 cm (or 4 ⁶/₇ cm)
The area of a trapezoid is 70.55 sq ft. The parallel bases are 8.2 ft and 10.8 ft. Determine the perpendicular height of the trapezoid.
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Step 2: Double the area = 2 × 70.55 = 141.1
Step 3: Divide by sum of bases: h = 141.1 / 19.0 = 7.426 ft (or ~7.43 ft)
A trapezoid has an area of 120 cm² and a height of 10 cm. If the longer parallel base is 16 cm, find the length of the shorter parallel base.
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120 = 5 × (a + 16)
Divide both sides by 5: 24 = a + 16
Subtract 16: a = 24 - 16 = 8 cm
The parallel sides of a trapezium are in the ratio 3 : 5 and the distance between them is 12 cm. If the area is 384 cm², find the lengths of both parallel sides.
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Area = ½ × (3x + 5x) × 12 = ½ × 8x × 12 = 48x
48x = 384 → x = 384 / 48 = 8
Shorter base = 3 × 8 = 24 cm
Longer base = 5 × 8 = 40 cm
The median (mid-segment) of a trapezoid is equal to m = ½(a + b). If a trapezoid has a median length of 14.5 meters and a height of 8 meters, calculate its area.
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Area = 14.5 × 8 = 116 m²
A metal sheet is in the shape of a trapezoid with bases 20 cm and 30 cm, and height 15 cm. A circular hole of radius 5 cm is punched through the center. Calculate the remaining area of the sheet. (Use π ≈ 3.1416)
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Circle Area = π r² = 3.1416 × 5² = 78.54 cm²
Remaining Area = 375 - 78.54 = 296.46 cm²