Lesson 5.4Composite Figures
Start hereWords, worked example, and sentence starters
Learning target 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.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| Composite FigureSpanish: Figura compuesta | A shape made by putting two or more simple shapes together. | rectangle + triangle |
| DecomposeSpanish: Descomponer | To break a shape into smaller, simpler shapes. | L shape → 2 rectangles |
| AddSpanish: Sumar | Add up the areas of the smaller shapes to get the total. | roof + wall |
| SubtractSpanish: Restar | Take away the area of a missing piece from a bigger shape. | wall − window |
| FormulaSpanish: Fórmula | A math rule written with symbols. | Rectangle: A = l × w; Triangle: A = ½ × b × h; use the right formula for each piece of a composite figure |
| Regular polygonSpanish: Polígono regular | A shape whose sides are all the same length and whose angles are all the same size. | A stop sign is a regular octagon. |
How it worksWorked examplearea of a figure with a piece removed
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A banner starts as a rectangle 18 in. by 12 in. A triangle with base 8 in. and height 6 in. is cut out of one end. Find the area left.
- Find the area of the whole rectangle. 18 × 12 = 216
- Find the area of the piece that was removed. ½ × 8 × 6 = 24
- The piece is gone, so subtract. 216 − 24 = 192
Answer: The banner covers 192 square inches (192 in²).
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
An L-shaped rug decomposes into a 16 ft by 9 ft rectangle and a 7 ft by 3 ft rectangle. Find the total area.
- Sketch the rug and draw the one line that splits it into two rectangles.
- Piece 1: × = ft² Piece 2: × = ft²
- Add or subtract? Total: + = ft²
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- I decomposed the figure into and .
- The pieces have areas of and .
- I the two areas because .
- The total area is square units.
Word bank composite figuredecomposepiecerectangletriangleaddsubtractcut-outremovedtotalareasquare units
Watch outA common mistake
A common mistake in Area of Composite Figures is adding every piece even when a piece has been cut out of the figure. For a 10 ft by 8 ft rectangle with a 3 ft by 2 ft rectangular notch cut from one corner, students compute the full rectangle 10 × 8 = 80 sq ft and stop, or they add the notch instead of removing it (80 + 6 = 86 sq ft) instead of subtracting it: 80 − (3 × 2) = 80 − 6 = 74 sq ft. Before submitting, check whether each piece is part of the figure (add it) or missing from the figure (subtract it).
Lesson 5.4Composite Figures
Apply Day · Version ASupported practice
Learning target 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.
-
1Complete each step, then write the final answer.
A shape is made of a 6 m by 3 m rectangle joined to a 2 m by 5 m rectangle. Find its total area.
Show your workHint Find each rectangle. They are joined, so add.
Final answer: -
2Complete each step, then write the final answer.
A rectangle is 8 ft by 5 ft. A 2 ft by 2 ft square is cut out of it. Find the area that is left.
Show your workHint The square is cut out, so subtract it.
Final answer: -
3Complete each step, then write the final answer.
A regular hexagon splits into 6 congruent triangles. Each triangle has an area of 9 square inches. Find the area of the hexagon.
Show your workHint All 6 triangles are the same. Multiply.
Final answer:
Lesson 5.4Composite Figures
Apply Day · Version BCore practice
Learning target 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.
-
1Complete each step, then write the final answer.
A regular pentagon splits into 5 congruent triangles. Each has a base of 6 cm and a height of 4 cm. Tom says the area of the pentagon is 12 square centimeters. What is the correct area?
Show your workFinal answer: -
2Complete each step, then write the final answer.
A regular polygon splits into congruent triangles that meet at the center. Each triangle has a base of 5 cm and a height of 6 cm. The polygon’s area is 120 square centimeters. How many sides does it have?
Show your workFinal answer: -
3Complete each step, then write the final answer.
An L-shape is made of an 8 cm by 3 cm rectangle and a 2 cm by 4 cm rectangle. Find its total area.
Show your workFinal answer:
Lesson 5.4Composite Figures
Apply Day · ChallengeExtension
Learning target 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.
-
1Circle the letter of the best answer. Show how you know.
An L-shaped room splits into two rectangles: one is 12 feet by 8 feet, the other is 6 feet by 5 feet. What is the total floor area?
- A30 square feet
- B62 square feet
- C96 square feet
- D126 square feet
FormulaPut the numbers inWork it outAnswer with its unit -
2Complete each step, then write the final answer.
An L-shape fits in a 10 ft by 8 ft rectangle with a 4 ft by 4 ft corner missing. Ana adds two pieces and gets 58 square feet. Ben gets 64 square feet. What is the correct area?
Show your workFinal answer: -
3Complete each step, then write the final answer.
An L-shape fits in a 9 cm by 7 cm rectangle. A 3 cm by 2 cm corner is cut out. Find the area of the L-shape.
Show your workFinal answer: