Question

topic 10 block 10 homework name 4. can you solve the sailboat puzzle? what is the total area of the seven pieces that make up the sailboat? draw the design on centimeter grid paper. then cut out the pieces and rearrange them in a single shape with known area. you may have to cut and rearrange parts of individual pieces in order to solve the puzzle.

Explanation:

Step1: Calculate area of Piece 1

Piece 1 is a 1x1 square: $A_1 = 1 \times 1 = 1$

Step2: Calculate area of Piece 2

Piece 2 is a parallelogram with base=3, height=1: $A_2 = 3 \times 1 = 3$

Step3: Calculate area of Piece 3

Piece 3 is a rhombus (4 right triangles, each 1x1): $A_3 = 4 \times \frac{1 \times 1}{2} = 2$

Step4: Calculate area of Piece 4

Piece 4 is a parallelogram with base=3, height=1: $A_4 = 3 \times 1 = 3$

Step5: Calculate area of Piece 5

Piece 5 is a right triangle with legs=1,1: $A_5 = \frac{1 \times 1}{2} = 0.5$

Step6: Calculate area of Piece 6

Piece 6 is a right triangle with legs=1,1: $A_6 = \frac{1 \times 1}{2} = 0.5$

Step7: Calculate area of Piece 7

Piece 7 is a rhombus (4 right triangles, each 1x1): $A_7 = 4 \times \frac{1 \times 1}{2} = 2$

Step8: Sum all individual areas

Total area: $A_{total} = 1 + 3 + 2 + 3 + 0.5 + 0.5 + 2$

Answer:

The total area of the seven pieces is 12 square centimeters. When rearranged, these pieces can form a 3x4 rectangle (or other shapes with an area of 12 square centimeters).