Area of Trapezoids

Show your work for each problem.

1.
What is the formula for the area of a trapezoid?
1. a)
2. b)
3. c)
4. d)
Answer:
The correct formula is . This finds the average of the two bases and multiplies by the height.
2.
In a trapezoid, what are the 'bases'?
1. a)The two parallel sides
2. b)The two non-parallel sides
3. c)All four sides
4. d)The height and one side
Answer: The two parallel sides
The bases of a trapezoid are the two parallel sides. They are called bases because they form the 'top' and 'bottom' of the shape.
3.
A trapezoid has bases of 6 cm and 10 cm, and a height of 4 cm. What is the area in cm²?
Answer: 32
cm²
4.
Find the area of a trapezoid with bases 5 m and 9 m, and height 6 m. Answer in m².
Answer: 42
m²
5.
Calculate the area of a trapezoid with bases 8 cm and 12 cm, and height 5 cm.
Answer: 50
1. What is the sum of the two bases (8 + 12)? 20
2. Multiply this sum by the height (20 × 5) 100
3. Divide by 2 to get the final area 50
6.
A trapezoid has bases of 7 m and 11 m, with a height of 8 m. What is its area?
1. a)72 m²
2. b)88 m²
3. c)56 m²
4. d)144 m²
Answer: 72 m²
m². The answer 144 m² is wrong because it forgets to divide by 2.
7.
A trapezoidal garden has parallel sides of 4.5 m and 7.5 m, with a perpendicular distance of 6 m. What is the area in m²?
Answer: 36
m²
8.
A roof section is trapezoidal with parallel edges of 5 m (top) and 9 m (bottom), and height 3 m. Find the area.
Answer: 21
1. Add the two parallel edges (5 + 9) 14
2. Multiply by the height (14 × 3) 42
3. Divide by 2 to get the area in m² 21
9.
Calculate the area of a trapezoid with bases of 3.5 cm and 6.5 cm, and height of 4 cm.
Answer: 20
1. What is 3.5 + 6.5? 10
2. What is 10 × 4? 40
3. What is 40 ÷ 2? 20
10.
Which measurement must be perpendicular to both bases when calculating trapezoid area?
1. a)The height
2. b)One of the bases
3. c)The slant side
4. d)The perimeter
Answer: The height
The height must be perpendicular to both bases. This is different from the slant sides, which are not perpendicular to the bases.
11.
A trapezoid has an area of 60 cm², a height of 8 cm, and one base of 5 cm. What is the other base in cm?
Answer: 10
→ → → cm
12.
A trapezoid has an area of 54 m², bases of 6 m and 12 m. Find the height.
Answer: 6
1. What is the sum of the bases (6 + 12)? 18
2. Set up: 54 = 18 × h / 2. Multiply both sides by 2. What is 54 × 2? 108
3. Now we have 108 = 18 × h. Divide 108 by 18 to find h. 6
13.
A swimming pool is trapezoid-shaped with widths of 8 m and 14 m at opposite ends, and length of 25 m. What is the surface area in m²?
Answer: 275
The pool's surface area = m²
14.
A trapezoid has an area of 84 cm², height of 7 cm, and one base is twice the other. Find both bases.
Answer: 8 and 16
1. Let smaller base = x, larger = 2x. What is x + 2x? 3x
2. 84 = (3x × 7) / 2. Multiply both sides by 2. What is 84 × 2? 168
3. 168 = 21x. What is 168 ÷ 21? 8
4. If x = 8, what is 2x (the larger base)? 16
15.
If both bases of a trapezoid are doubled while the height stays the same, how does the area change?
1. a)The area doubles
2. b)The area triples
3. c)The area stays the same
4. d)The area quadruples
Answer: The area doubles
Original: . If both bases double: . The area doubles.
16.
What is the area of a trapezoid with bases 15 cm and 25 cm, and height 8 cm? Answer in cm².
Answer: 160
cm²
17.
A trapezoid has bases of 4 m and 6 m with a height of 3 m. Find the area step by step.
Answer: 15
1. Add the two bases: 4 + 6 = ? 10
2. Multiply by height: 10 × 3 = ? 30
3. Divide by 2: 30 ÷ 2 = ? 15