Determine the Area of Trapezoids

Apply the trapezoid area formula A = ½(b₁ + b₂)h and decompose trapezoids into simpler shapes.

6.GR.A.1 · Area, Surface Area & Volume
Level
Guided practice with vocabulary support

🟠 Level 0 — Extra Support

Sentence starters: “First, I…” · “The answer is… because…” · “I know this because…”
W

Warm-Up

2 questions
Warm-Up 1
A trapezoid has exactly how many pairs of parallel sides?
Vocabulary: A trapezoid is a quadrilateral with exactly one pair of parallel sides. These parallel sides are called the bases (b₁ and b₂).
b₁ (longer base) b₂ (shorter base) h
✓Correct! A trapezoid has exactly one pair of parallel sides, called the bases.
✗A trapezoid has exactly 1 pair of parallel sides. The answer is B.
Warm-Up 2
What is the formula for the area of a trapezoid?
Key idea: The height (h) is the perpendicular distance between the two parallel bases. The formula uses the sum of both bases.
✓Correct! A = ½(b₁ + b₂) × h. You add both bases, multiply by the height, then take half.
✗The trapezoid formula is A = ½(b₁ + b₂)h. The answer is B.
P

Practice

5 questions
Practice 1
Find the area of the trapezoid. The parallel bases are 6 cm and 10 cm, and the height is 4 cm.
Steps: 1) Add the bases: 6 + 10 = 16. 2) Multiply by the height: 16 × 4 = 64. 3) Take half: 64 ÷ 2 = 32.
10 cm 6 cm 4 cm
A = cm²

Sentence frame: "A = ½(___ + ___) × ___ = ½ × ___ × ___ = ___."

✓Correct! A = ½(6 + 10) × 4 = ½ × 16 × 4 = 32 cm².
✗A = ½(6 + 10) × 4 = ½ × 64 = 32 cm².
Practice 2
A trapezoid has bases of 14 ft and 8 ft, and a height of 5 ft. What is its area?
Formula: A = ½(b₁ + b₂)h. Substitute: A = ½(14 + 8) × 5.
Show your work:

Sentence frame: "A = ½(___ + ___) × ___ = ___ ft²."

✓Correct! A = ½(14 + 8) × 5 = ½ × 22 × 5 = 55 ft².
✗A = ½(14 + 8) × 5 = ½ × 110 = 55 ft². The answer is B.
Practice 3
Match each trapezoid measurement set with the correct area.
Strategy: For each set, use A = ½(b₁ + b₂)h. Add the bases, multiply by height, divide by 2.
40 cm²
54 m²
30 in.²
b₁=6, b₂=4, h=6 in.
b₁=12, b₂=8, h=4 cm
b₁=10, b₂=8, h=6 m
✓All correct! ½(6+4)×6=30, ½(12+8)×4=40, ½(10+8)×6=54.
✗Check your calculations. Use A = ½(b₁+b₂)h for each. Try again!
Practice 4
A trapezoid can be decomposed into a rectangle and two triangles. If the bases are 12 m and 8 m, and the height is 5 m, what is the area of the rectangle in the middle?
Decompose: The rectangle in the middle has a width equal to the shorter base (8 m) and the same height (5 m). The two triangles on the sides make up the rest.
rectangle triangle triangle 12 m 8 m 5 m
Rectangle area = m²

Sentence frame: "The rectangle has width ___ and height ___, so its area is ___ × ___ = ___."

✓Correct! Rectangle area = 8 × 5 = 40 m².
✗The rectangle uses the shorter base (8 m) as width and the height (5 m). Area = 8 × 5 = 40 m².
Practice 5
A trapezoid has an area of 45 in.², a height of 5 in., and one base of 7 in. What is the length of the other base?
Strategy: Use A = ½(b₁ + b₂)h. Substitute what you know and solve for the missing base.
b₂ = in.
Show your work:

Sentence frame: "45 = ½(7 + b₂) × 5. So 45 = ½ × 5 × (7 + b₂). Solving: b₂ = ___."

✓Correct! 45 = ½(7 + b₂) × 5 → 90 = (7 + b₂) × 5 → 18 = 7 + b₂ → b₂ = 11 in.
✗45 = ½(7 + b₂)(5). Multiply both sides by 2: 90 = 5(7 + b₂). Divide by 5: 18 = 7 + b₂. So b₂ = 11 in.
★

Challenge

1 question
Challenge
A trapezoid is decomposed into two triangles by drawing one diagonal. The bases are 10 m and 6 m, and the height is 8 m. What is the sum of the two triangles' areas? Does it match the trapezoid formula?
Think about it: Triangle 1 uses base b₁ = 10 and height 8. Triangle 2 uses base b₂ = 6 and height 8. Find each area with A = ½bh, then add them.
Triangle 1 Triangle 2 10 m 6 m 8 m
Total area = m²
Show both triangles and verify with the formula:

Sentence frame: "Triangle 1 = ½ × ___ × ___ = ___. Triangle 2 = ½ × ___ × ___ = ___. Total = ___. Formula: ½(___ + ___) × ___ = ___."

✓Excellent! T1 = ½(10)(8) = 40. T2 = ½(6)(8) = 24. Total = 64 m². Formula: ½(10+6)(8) = 64 m². They match!
✗T1 = ½(10)(8) = 40. T2 = ½(6)(8) = 24. Total = 40 + 24 = 64 m².