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Geometry and Measurement 6-8 / Week 01 / Thursday
4/6
Week 01 · Area by Cutting and Composing

Thursday

The floor plan
// Cut a shape apart, slide it together, count the squares
⏱ about 20 min

Thursday: The Floor Plan

Rocket unrolls the clubhouse floor plan across the Blueprint Table. "Four rooms. Four shapes. One big area."

"A rectangle, a triangle, a trapezoid and a parallelogram," Raven reads. "All measured in centimeters, on the model."

"What do you notice about the storage corner?" she asks, pointing at an L shape.

Rocket frowns. "It is not any of our shapes." Then he brightens. "But it is two rectangles."

Nova hovers over the L, her light drawing a line across it. "Cut it in your head," she says. "Then add."

"Decompose," Raven says. "Cut it into pieces you know, find each area, add them up."

Rocket is already writing. "Six by two, plus three by three. Twenty-one squares." Nova hums. "Now the whole floor."

Decompose any polygon

An L-shaped polygon on a grid, six corners lettered A to F

Any polygon can be cut into rectangles and triangles. Find each piece's area and add them. This is called decomposing.

The L shape is a 6 by 2 rectangle below a 3 by 3 square. Its area is 12 + 9 = 21 square units.

You can also cut it the other way: a 3 by 5 rectangle beside a 3 by 2 rectangle. The total is the same.

Raven's floor plan table

The crew's own measurements of the model clubhouse floor, in centimeters, from Raven's Blueprint Book.

RoomShapeMeasurements (cm)Area (sq cm)
Main roomrectanglebase 30, height 20600
Porchtrianglebase 20, height 12120
Side roomtrapezoidtop 10, bottom 20, height 8120
Entryparallelogrambase 10, height 660

The main room is 30 × 20 = 600. The porch triangle is ½ × 20 × 12 = 120.

Add all four rooms and the whole floor is 900 square centimeters of cardboard.

READ THE FLOOR PLAN
  • Read the question.
  • Tap your answer.
A triangle with base 20 cm and height 12 cmThe porch is a triangle with base 20 cm and height 12 cm. What is its area in square centimeters?
A trapezoid with base 20 cm, top 10 cm and height 8 cmThe side room is a trapezoid: top 10, bottom 20, height 8 cm. What is its area in square centimeters?
A parallelogram with base 10 cm and height 6 cmThe entry is a parallelogram with base 10 cm and height 6 cm. What is its area in square centimeters?
What is the area of the main room and the porch together, in square centimeters?
DECOMPOSE THE STORAGE CORNER
  • Read the question.
  • Tap your answer.
An L-shaped polygon on a grid, six corners lettered A to FWhat is the area of the polygon in square units?
An L-shaped polygon on a grid, a 5 by 3 rectangle with a 2 by 1 piece on topNova draws another L: a 5 by 3 rectangle with a 2 by 1 piece on top. What is its area in square units?
A five-sided polygon on a grid: a rectangle 6 by 3 with a triangle on topThe clubhouse end wall is a rectangle with a triangle roof on top. What is its area in square units?
What is the area of the main room in square centimeters? Type the number.
What is the area of the whole clubhouse floor, all four rooms, in square centimeters? Type the number.
How many square units does the L-shaped storage corner cover? Type the number.
From the floor planTrue or false?
An L shape can be cut into two rectangles.?
Cutting the L shape a different way gives a different area.?
12 + 9 = 21?
The whole floor area is the sum of the four room areas.?
WHY THIS EXERCISEThe same squares are counted no matter where you cut, so every decomposition agrees.
Try it
On grid paper, outline a shape with six or eight corners, all right angles. Cut it into rectangles two different ways.
Find the area each way. Write both in your Blueprint Book and compare.
Draw the L-shaped storage corner and show two different ways to cut it into rectangles.

Four rooms, one total. Tomorrow you find cut-and-compose shapes all around you and review the week.

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