Warm-Up 1
A triangle is half of what shape?
Key idea: If you copy a
triangle and flip it, the two triangles
form a parallelogram. So a triangle is
exactly half a parallelogram.
✓Correct! A triangle is exactly half of a parallelogram. That is why
the area formula has ½.
✗Two copies of the same triangle fit together to make a
parallelogram. The answer is
B.
Warm-Up 2
Which formula gives the area of a triangle?
Vocabulary: The area of a
triangle is half the area of a parallelogram with the same
base and height.
✓Correct! The area of a triangle is A = ½ × b ×
h.
✗Since a triangle is half a parallelogram, its area is
A = ½bh. The answer is
B.
Practice 1
Find the area of the triangle below.
Formula:
A = ½ × b × h. Identify
the base and the perpendicular height, then multiply and divide by 2.
A =
cm²
Sentence frame: "A = ½ × ___ × ___ = ___
cm²."
✓Correct! A = ½ × 10 × 7 = 35 cm².
✗Use A = ½ × 10 × 7 = ½ × 70 =
35 cm².
Practice 2
A right triangle has legs of 6 in. and 8 in. What is the area?
Hint: In a right triangle, the two
legs are the base and the height (they meet
at a right angle). Use A = ½bh.
Sentence frame: "The legs are ___ and ___, so A = ½ ×
___ × ___ = ___."
✓Correct! A = ½ × 6 × 8 = 24 in.².
✗A = ½ × 6 × 8 = ½ × 48 =
24 in.². The answer is
B.
Practice 3
Which line segment represents the height of this
triangle?
Remember: The height is
the perpendicular distance from the base to
the opposite vertex. It forms a right angle with the base.
✓Correct! The height is the perpendicular segment from the top
vertex straight down to the base (Line A). Notice the right-angle
mark.
✗The height must be perpendicular to the base.
Line A is the only segment that forms a right angle
with the base.
Practice 4
A triangle has a base of 16 m and a height of 9 m. What is its area?
Steps: 1) Write the formula:
A = ½bh. 2) Substitute: A = ½
× 16 × 9. 3) Calculate.
A =
m²
Sentence frame: "A = ½ × ___ × ___ = ___."
✓Correct! A = ½ × 16 × 9 = ½ × 144 =
72 m².
✗A = ½ × 16 × 9 = ½ × 144 =
72 m².
Practice 5
A triangular banner has an area of 60 in.² and a base of 12 in.
What is the height of the banner?
Strategy: Start with
A = ½bh. Substitute what you know:
60 = ½ × 12 × h. Solve for h.
h =
in.
Sentence frame: "60 = ½ × 12 × h, so 60 = ___
× h, and h = ___."
✓Correct! 60 = ½ × 12 × h → 60 = 6h → h
= 10 in.
✗60 = ½ × 12 × h → 60 = 6h → h = 60
÷ 6 = 10 in.
Challenge
A parallelogram has a base of 14 ft and a height of 10 ft. A diagonal
divides it into two equal triangles. What is the area of
one triangle?
Think about it: First find the area of the
parallelogram (A = bh). Then, since the
diagonal splits it into two equal
triangles, divide by 2.
Area of one triangle =
ft²
Sentence frame: "The parallelogram has area ___ × ___ = ___.
One triangle is half: ___ ÷ 2 = ___."
✓Excellent! Parallelogram area = 14 × 10 = 140 ft². One
triangle = 140 ÷ 2 = 70 ft².
✗Parallelogram area = 14 × 10 = 140 ft². One triangle =
140 ÷ 2 = 70 ft².