Tangram Area
Weekly Problem 29 - 2008
The seven pieces in this 12 cm by 12 cm square make a Tangram set. What is the area of the shaded parallelogram?
The seven pieces in this 12 cm by 12 cm square make a Tangram set. What is the area of the shaded parallelogram?
Age
11 to 14
Challenge level
Problem
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The seven pieces in this $12 \; \text{cm} \times 12 \; \text{cm}$ square make a Tangram set. What is the area of the shaded parallelogram?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
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The parallelogram has base $6 \; \text{cm}$ and height $3 \; \text{cm}$, so area $6 \; \text{cm} \times 3 \; \text{cm} = 18\; \text{cm}^{2} $
Alternatively, notice that if you rearrange the parallelogram into a rectangle, you can tile the square with eight of them. Therefore the area of the parallelogram is $144 \div 8 = 18 \text{cm}^{2}$