Area of a Trapezoid Worksheet: Grade 8
Focus: Pythagorean theorem height derivation, 4 sides without height, coordinate trapezoids.
An isosceles trapezoid has parallel bases of 10 cm and 22 cm. The non-parallel equal legs each measure 10 cm. Height is NOT given. Calculate its area.
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Step 2: Pythagorean theorem for height h = √(leg² - x²) = √(10² - 6²) = √(100 - 36) = √64 = 8 cm
Step 3: Area = ½ × (10 + 22) × 8 = ½ × 32 × 8 = 128 cm²
A right-angled trapezoid has bases 15 m and 20 m. Its non-perpendicular slant leg measures 13 m. Find the area.
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Step 2: Height h = √(c² - x²) = √(13² - 5²) = √(169 - 25) = √144 = 12 m
Step 3: Area = ½ × (15 + 20) × 12 = ½ × 35 × 12 = 210 m²
The parallel sides of a trapezium are 25 m and 10 m. Its non-parallel sides are 14 m and 13 m. Find the area of the trapezium.
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Step 2: Semi-perimeter s = (15 + 14 + 13)/2 = 21 m
Step 3: Triangle Area via Heron's = √(21 × 6 × 7 × 8) = √7056 = 84 m²
Step 4: Height h = 2 × Area / base = (2 × 84) / 15 = 168 / 15 = 11.2 m
Step 5: Trapezoid Area = ½ × (25 + 10) × 11.2 = ½ × 35 × 11.2 = 196 m²
A trapezoid has vertices at coordinates A(2, 2), B(8, 2), C(6, 7), and D(3, 7). Find its area.
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Top base CD length = 6 - 3 = 3 units (along y = 7)
Vertical height h = 7 - 2 = 5 units
Area = ½ × (6 + 3) × 5 = ½ × 9 × 5 = 22.5 units²
The two diagonals of a quadrilateral trapezoid are 16 cm and 20 cm. They intersect at an angle of 30°. Find the area. (Use sin(30°) = 0.5)
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Area = 0.5 × 16 × 20 × sin(30°)
Area = 0.5 × 320 × 0.5 = 80 cm²
A water trough is a trapezoidal prism 3 meters long. Its cross-section trapezoid has top base 1.2 m, bottom base 0.8 m, and depth 0.6 m. Find the volume of water the trough can hold in cubic meters (m³) and liters. (1 m³ = 1000 L)
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Volume = Area × Length = 0.6 × 3 = 1.8 m³
Capacity in liters = 1.8 × 1000 = 1,800 Liters