Trapezoid Area Practice Questions & Answers
Test your mastery of trapezoids and trapeziums across all question types: basic base-height, reverse algebra (find missing height/base), Pythagorean slant legs, and composite shapes.
Find the area of a trapezoid with bases 9 cm and 15 cm and height 8 cm.
Calculate the surface area enclosed in cm².
Show Full Solution & Proof
1. Formula: A = ½ × (a + b) × h
2. Substitute values: A = ½ × (9 + 15) × 8
3. Add inside parentheses: 9 + 15 = 24 cm
4. Multiply: A = ½ × 24 × 8 = 12 × 8 = 96 cm²
A trapezoid has bases 12.4 m and 17.6 m. Its perpendicular height is 6.5 m.
Calculate the area in square meters (m²).
Show Full Solution & Proof
1. Sum bases: 12.4 + 17.6 = 30.0 m
2. Multiply by height: 30.0 × 6.5 = 195.0
3. Divide by 2: 195.0 / 2 = 97.5 m²
The area of a trapezoid is 180 sq inches. Its bases are 14 in and 22 in. Find the height.
Calculate height h in inches.
Show Full Solution & Proof
1. Formula: h = (2 × Area) / (a + b)
2. 2 × 180 = 360
3. a + b = 14 + 22 = 36 in
4. h = 360 / 36 = 10 inches
A trapezoid with area 84 cm² has height 7 cm and bottom base 16 cm. Find top base a.
Calculate missing base a in cm.
Show Full Solution & Proof
1. Formula: a = (2 × Area / h) - b
2. (2 × 84) / 7 = 168 / 7 = 24
3. a = 24 - 16 = 8 cm
An isosceles trapezoid has bases 10 cm & 18 cm, and legs 5 cm each. Find its area.
Height is not given! Use Pythagoras to find h first.
Show Full Solution & Proof
1. Overhang x = (18 - 10) / 2 = 8 / 2 = 4 cm
2. Height h = √(5² - 4²) = √(25 - 16) = √9 = 3 cm
3. Area = ½ × (10 + 18) × 3 = ½ × 28 × 3 = 14 × 3 = 42 cm²
A concrete barrier is a trapezoidal prism 2 meters long with bases 0.6 m and 0.4 m, and height 0.8 m. Find its volume in m³.
Calculate 3D solid volume in cubic meters.
Show Full Solution & Proof
1. Trapezoid Base Area = ½ × (0.6 + 0.4) × 0.8 = ½ × 1.0 × 0.8 = 0.4 m²
2. Volume = Area × Length = 0.4 m² × 2 m = 0.8 m³
Calcolatori Specifici per il Trapezio
Calcola area, perimetro e misure mancanti per qualsiasi trapezio e applicazione pratica.