Determine the Area of Parallelograms and Rhombuses
Derive and apply area formulas for parallelograms (A = bh) and
rhombuses (A = d₁ × d₂ ÷ 2).
6.GR.A.1 · Area, Surface Area & Volume
Level
Guided practice with vocabulary support
🟠 Level 0 — Extra Support
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One at a time: answer one question, check it, then go on.
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Sentence starters: “First, I…” · “The answer is… because…” · “I know this because…”
W
Warm-Up
2 questions
Warm-Up 1
Which measurement do you need to find the area of a
parallelogram?
Vocabulary: A
parallelogram is a four-sided shape with
two pairs of parallel sides. To find its
area, you need the
base and the
height (the perpendicular distance between
the bases).
✓Correct! The area of a parallelogram uses the formula A = base
× height.
✗Not quite. To find the area of a parallelogram, you need the
base and the perpendicular height.
A = b × h. The answer is A.
Warm-Up 2
A parallelogram has a base of 10 cm and a height of 6 cm. What is its
area?
Formula:A = b × h.
Multiply the base by the height.
✓Correct! A = 10 × 6 = 60 cm².
✗Use A = b × h. That gives 10 × 6 = 60 cm². The
answer is C.
P
Practice
5 questions
Practice 1
Find the area of the parallelogram below.
Remember:Area = base × height. Use the
perpendicular height, not the slant side.
A =in.²
Show your work:
Sentence frame: "The area is ___ × ___ = ___ square inches."
✓Correct! A = 14 × 8 = 112 in.². Remember to use the
height (8 in.), not the slant side (10 in.).
✗Use the base (14 in.) and the height (8 in.), not the slant side. A
= 14 × 8 = 112 in.².
Practice 2
A rhombus has diagonals of 12 m and 8 m. What is its
area?
Vocabulary: A rhombus has
four equal sides and its diagonals cross at right angles.
Area = (d₁ × d₂) ÷ 2.
Explain your reasoning:
Sentence frame: "The diagonals are ___ and ___. A = (___ ×
___) ÷ 2 = ___."
✓Correct! A = (12 × 8) ÷ 2 = 96 ÷ 2 = 48
m².
✗Use A = (d₁ × d₂) ÷ 2. A = (12 × 8)
÷ 2 = 96 ÷ 2 = 48 m². The answer
is B.
Practice 3
Sort each formula to the correct shape.
Remember:Parallelogram: A
= base × height. Rhombus: A =
(d₁ × d₂) ÷ 2. A
rectangle is a special parallelogram, so A
= l × w.
A = b × h
A = (d₁ × d₂) ÷ 2
A = 9 × 5 = 45
A = (6 × 10) ÷ 2 = 30
A = 12 × 7 = 84
A = (8 × 14) ÷ 2 = 56
Parallelogram
Rhombus
✓All correct! Parallelogram uses A = bh. Rhombus uses A = (d₁
× d₂) ÷ 2.
✗Some items are in the wrong group. Parallelogram formulas use base
× height. Rhombus formulas use diagonals. Try again!
Practice 4
A parallelogram has an area of 72 ft² and a base of 9 ft. What is
its height?
Strategy: Use
A = b × h. You know A and b, so solve
for h: h = A ÷ b.
h =ft
Show your work:
Sentence frame: "Since A = b × h, I can find h = A ÷ b
= ___ ÷ ___ = ___."
✓Correct! h = 72 ÷ 9 = 8 ft.
✗Use h = A ÷ b = 72 ÷ 9 = 8 ft.
Practice 5
Mr. Neft is designing a parallelogram-shaped garden plot with a base
of 15 ft and a height of 8 ft. How many square feet of soil does he
need to cover the entire garden?
Real-world connection: The garden is shaped like a
parallelogram. Use
A = b × h to find how much soil is
needed.
Explain your answer:
Sentence frame: "Mr. Neft needs ___ square feet of soil because A =
___ × ___ = ___."
✓Correct! A = 15 × 8 = 120 ft². Mr. Neft needs 120 square
feet of soil.
✗Use A = b × h = 15 × 8 = 120 ft².
The answer is C.
★
Challenge
1 question
Challenge
A rhombus-shaped tile has an area of 54 cm². One diagonal is 9 cm
long. What is the length of the other diagonal?
Think about it: Use
A = (d₁ × d₂) ÷ 2.
You know A = 54 and d₁ = 9. Solve for d₂.
d₂ =cm
Show your work step by step:
Sentence frame: "I used A = (d₁ × d₂) ÷ 2.
Substituting: 54 = (9 × d₂) ÷ 2. So d₂ =
___."