Lesson 4: Apply Area Concepts to Solve Problems6.GR.1

I can…

I can find the area of a composite figure by decomposing it into basic shapes, including a regular polygon split into triangles, and adding or subtracting the areas.

Key words

• Area of Composite Figures — The total space inside a figure made of basic shapes. Formula: A = A₁ + A₂ — add the parts (or subtract a missing piece).
• Composite Figure — A shape made by putting two or more simple shapes together.
• Decompose — To break a shape into smaller, simpler shapes.
• Add — Add up the areas of the smaller shapes to get the total.
• Subtract — Take away the area of a missing piece from a bigger shape.
• Formula — A math rule written with symbols.

Steps

1. My L-shaped room splits into two rectangles: one is 12 ft by 8 ft, the other is 6 ft by 5 ft.
2. First rectangle: A = length × width = 12 × 8 = 96 square feet.
3. Second rectangle: A = 6 × 5 = 30 square feet.
4. The pieces are joined, so I add: 96 + 30 = 126.
5. So the total area is 126 square feet.

Try it

A composite figure is made of a 9 ft x 7 ft rectangle and a 3 ft x 4 ft rectangle joined together. What is the total area?

Check your answer

75 sq ft

Area 1 = 9 x 7 = 63 sq ft. Area 2 = 3 x 4 = 12 sq ft. Total = 63 + 12 = 75 square feet.

Sentence starter

I know ___ because ___.

Goal: I can explain my steps using the words composite figure, decompose, add, and subtract.