Lesson 5.45.4 Small Group · Group 1
Start hereWords, worked example, and sentence starters
Learning target With my small group, 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 — one step at a time, with support.
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. | triangles joined together |
| DecomposeSpanish: Descomponer | To break a shape into smaller, simpler shapes. | hexagon → 6 triangles |
| AddSpanish: Sumar | Add up the areas of the smaller shapes to get the total. | T-shaped hallway: top rectangle = 30 sq ft, bottom rectangle = 28 sq ft → total = 30 + 28 = 58 sq ft |
| SubtractSpanish: Restar | Take away the area of a missing piece from a bigger shape. | A 14×10 pool with a 6×4 cutout: 140 − 24 = 116 sq ft of water surface |
| 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. | stop sign, hexagon tile |
How it worksWorked examplearea of a regular polygon
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A regular octagon has sides of 12 in. A triangle drawn from the center to one side has a height of 14 in. Find the area.
- A regular octagon has eight equal sides, so it decomposes into eight congruent triangles.
- Find the area of ONE triangle. ½ × 12 × 14 = 84
- Every triangle matches, so multiply by how many there are. 84 × 8 = 672
Answer: The area of the octagon is 672 square inches (672 in²).
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A regular hexagon has sides of 20 m. Each triangle drawn from the center has a height of 17 m. Find the area.
- How many congruent triangles does a regular hexagon decompose into?
- Area of ONE triangle. ½ × × =
- Multiply by the number of triangles. × =
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 congruent .
- The area of one triangle is square units.
- There are triangles, so the total area is .
- I know the triangles are congruent because .
Word bank regular polygondecomposecongruenttrianglecenterbaseheightmultiplytotalareasquare unitscomposite figure
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 5.45.4 Small Group · Group 1
Group 1Supported practice
Learning target With my small group, 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 — one step at a time, with support.
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1Complete each step, then write the final answer.
Split the L into rectangle 1 and rectangle 2. An L-shaped floor is made of a 9 m by 4 m rectangle and a 3 m by 5 m rectangle. Find its area.
- 1What is the area of rectangle 1?
- 2What is the area of rectangle 2?
- 3The pieces are joined. What is the total area?
Final answer: -
2Complete each step, then write the final answer.
One of the 6 congruent triangles. A regular hexagon splits into 6 congruent triangles that meet at the center. Each triangle has a base of 8 inches and a height of 7 inches. Find the area of the hexagon.
- 1Find the area of one triangle.
- 2How many congruent triangles are there?
- 3Multiply. What is the area of the hexagon?
Final answer: -
3Complete each step, then write the final answer.
A shape is made of a 4 ft by 2 ft rectangle joined to a 2 ft by 2 ft square. Find its total area.
Show your workHint Find the area of each piece. They are joined, so add.
Final answer: -
4Complete each step, then write the final answer.
A house shape is a 10 ft by 8 ft rectangle with a triangle on top. The triangle has a base of 10 ft and a height of 6 ft. Find the total area.
Show your workHint Find the rectangle and the triangle separately. Remember the half for the triangle.
Final answer: -
5Complete each step, then write the final answer.
A wall is 12 ft wide and 9 ft tall. It has a window that is 3 ft by 4 ft. The window is not painted. How many square feet of wall need paint?
Show your workHint Find the whole wall. Then take away the window.
Final answer: -
6Complete 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 workHint Tom found the area of one piece. How many pieces make the pentagon?
Final answer:
Explain your thinkingHow do you decide whether to add or subtract the pieces of a shape? Use the wall and the house shape.
Sentence starter I add when the pieces are ___. · I subtract when a piece is ___.