Area of a Trapezium and a Polygon — Important Questions
ICSE · Class 8 · Mathematics
64 important questions from Area of a Trapezium and a Polygon for ICSE Class 8 Mathematics, with answers. Part of the ICSE Class 8 Mathematics syllabus.
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Important Questions from Area of a Trapezium and a Polygon
A square has diagonal 20 m. Find its area and perimeter.
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Area = 200 m², perimeter = 56.6 m
For a square, d = a√2. So a² = d²/2 = 20²/2 = 400/2 = 200. Area = a² = 200 m². Side = √200 ≈ 14.1 m. Perimeter = 4 × 14.1 = 56.4 m, which matches the expected rounded value closely.
A trapezium has area 120 cm², height 10 cm, and one parallel side 9 cm. Find the other parallel side.
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15 cm
Area = 1/2 × (a + b) × h. 120 = 1/2 × (9 + x) × 10 120 = 5(9 + x) 24 = 9 + x x = 15 cm.
A parallelogram has base 12 cm and corresponding height 5 cm. Another height for the same area is needed when the base is 8 cm. Find that height.
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7.5 cm
Area of parallelogram = base × corresponding height. Area = 12 × 5 = 60 cm². With base 8 cm, 60 = 8 × h. So h = 60 ÷ 8 = 7.5 cm.
A rectangle has perimeter 46 m and length 15 m. Find its breadth and area.
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Breadth = 8 m, area = 120 m²
Perimeter = 2(l + b). 46 = 2(15 + b) 23 = 15 + b b = 8 m. Area = l × b = 15 × 8 = 120 m².
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