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Area of Triangles & Composite Shapes

Apply A = ½ × b × h for triangles and find area of composite figures by decomposing them into parts.

Bridge to Grade 6 Unit R5 · Lesson 4 Builds 6.G.1
Lesson progress: 0%
Why this matters for Grade 6: The Grade 6 geometry standard 6.G.1 asks students to "find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes." This lesson is the direct prerequisite: mastering A = ½ × b × h and breaking composite shapes apart.
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Learn It

Area of a Triangle

A triangle is exactly half of a rectangle with the same base and height. So its area is half the base times the height.

A = ½ × b × h
Example 1 — Triangle: b = 6, h = 4
base = 6 h=4
A = ½ × 6 × 4 = ½ × 24 = 12 square units
Example 2 — Composite Shape (Rectangle + Triangle on top)
8 4 h=3
Rectangle: A = 8 × 4 = 32 sq units
Triangle: A = ½ × 8 × 3 = 12 sq units
Total composite area = 32 + 12 = 44 square units
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Try It · Guided

Work These Together

1. Find the area of a triangle with base = 10 cm and height = 6 cm.

Hint

A = ½ × b × h = ½ × 10 × 6 = ½ × 60 = 30 square cm.

2. A triangle has base = 8 m and height = 5 m. What is its area in square meters?

Hint

A = ½ × 8 × 5 = ½ × 40 = 20 square meters.

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Practice · On Your Own

You Try

3. A sail on a boat is shaped like a triangle with base = 4 m and height = 9 m. What is the area of the sail in square meters?

Hint

A = ½ × 4 × 9 = ½ × 36 = 18 square meters.

4. Which formula gives the area of a triangle?

Hint

A triangle is half a rectangle. The rectangle's area is b × h, so the triangle's area is ½ × b × h.

5. A composite shape is made of a rectangle (6 × 5) and a triangle on top (base 6, height 4). What is the total area in square units?

Hint

Rectangle: 6 × 5 = 30. Triangle: ½ × 6 × 4 = 12. Total = 30 + 12 = 42 square units.

Exit Ticket

Show What You Know

6. Find the area of a triangle with base = 14 ft and height = 5 ft.

Hint

A = ½ × 14 × 5 = ½ × 70 = 35 square feet.

7. A composite figure has a rectangle (10 × 3) and a triangle (base 10, height 6). What is the total area in square units?

Hint

Rectangle: 10 × 3 = 30. Triangle: ½ × 10 × 6 = 30. Total = 30 + 30 = 60 square units.