Neft Teacher · Learn It

Unit 5 · Standard 6.GR.1

Apply Area Concepts to Solve Problems

Lesson 5-4 · Learn It — how the math works

Why we're learning this

Your architecture firm is calculating the floor area of an L-shaped room for a client's new home. The contractor needs the total area to order the correct amount of flooring. The room can be split into two rectangles: one is 12 feet by 8 feet and the other is 6 feet by 5 feet.

✱ Math Workbench

Learn It

How do we find the area of a composite figure?

A composite figure is a shape made of two or more simple shapes joined together. We decompose it into basic shapes, find each area, then add or subtract.

Picture itSee what the math looks like before you read about it

This is an L-shaped room from a floor plan. A dashed line splits it into two rectangles, and each part is labeled with its length and width.
Where you see this in real lifeThis is an L-shaped room from a floor plan. A dashed line splits it into two rectangles, and each part is labeled with its length and width.

Watch me solve itI do — read one step at a time

The problem looks like this
A triangle with a base of 14 and a perpendicular height of 18. base = 14 height = 18
  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 :96 + 30 = 126
  5. So the total area is 126 square feet.
  6. A splits the same way: a stop sign is a regular octagon, so I cut it into 8 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 triangles, so I multiply instead of adding eight times:134.1 × 8 = 1,072.8 square inches

Watch out — mistakes students make here

  • 12 sq ft is only the small 4 ft × 3 ft rectangle. Add the 10 ft × 6 ft rectangle too: 60 + 12 = 72.
  • 60 sq ft is only the large 10 ft × 6 ft rectangle. Add the 4 ft × 3 ft rectangle too: 60 + 12 = 72.
  • 20 sq ft is only the flower bed that is cut out. Subtract it from the whole patio: 150 − 20 = 130.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. Now an L-shape made of a 5 ft by 4 ft rectangle and a 3 ft by 2 ft rectangle.
  2. First rectangle:5 × 4 = 20 square feet
  3. Second rectangle:3 × 2 = 6 square feet
  4. Are they joined or cut out?
    Check this step
    Joined, so we :20 + 6 = 26 square feet

On your ownYou do — solve this one by yourself

Before you start, remember:

  • Remember: joined pieces, but a piece that is cut out.

Solve: An L-shaped room is made of two rectangles: 10 ft × 6 ft and 4 ft × 3 ft. What is the total area?

My answer

Stuck? Open one hint at a time.

Hint 1

The L-shape is already split into two rectangles for you: 10 × 6 and 4 × 3.

Hint 2

Find each rectangle's area separately with A = l × w, then combine — joined shapes mean adding.

Hint 3

Compute 10 × 6 and 4 × 3, then add the two results. Label your answer in sq ft.

Check my answer
✅ Answer: 72 sq ft
Area 1 = 10 × 6 = 60 sq ft. Area 2 = 4 × 3 = 12 sq ft. Total = 60 + 12 = 72 sq ft.

Turn & TalkSay it out loud with a partner

The L-shaped room splits into a 12 ft by 8 ft rectangle and a 6 ft by 5 ft rectangle. Why is it easier to find the area after you the L into two rectangles?

Try starting with:

  • We decompose the L-shape into ___ because ___.Descomponemos la forma de L en ___ porque ___.
  • After I split it, I can find each area using ___.Después de dividirla, puedo hallar cada área usando ___.
Use these wordscomposite figuredecomposeaddsubtractformula