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.
• Regular polygon — A shape whose sides are all the same length and whose angles are all the same size.
• Congruent — Exactly the same size and shape.

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.
6. A regular polygon splits the same way: a stop sign is a regular octagon, so I cut it into 8 congruent triangles that meet at the centre.
7. One triangle has a base of 14 9/10 inches and a height of 18 inches, so A = 1/2 × 14.9 × 18 = 134.1 square inches.
8. There are 8 congruent triangles, so I multiply instead of adding eight times: 134.1 × 8 = 1,072.8 square inches.

Try it

A family's patio is made of an 8 ft x 5 ft rectangle and a 2 ft x 3 ft rectangle joined together. What is the total area?

Check your answer

46 sq ft

Area 1 = 8 x 5 = 40 sq ft. Area 2 = 2 x 3 = 6 sq ft. Total = 40 + 6 = 46 square feet.

Sentence starter

I know ___ because ___.

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