Sam has 3 identical squares. He places one square on top of 2 squares as shown in the figure. What is the area of the overlap?
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Area of overlap is 88 sq. cm.
Step-by-step explanation:
See the diagram attached.
The required area is the polygon ABCDE (The pink zone).
So, we have to deduct the area of the triangle Δ DEF (Yellow zone) from the total square i.e. ABCF.
Now, area of the overlap = (10 × 10) - 0.5 × 3 × (10 + 10 - 6 - 6)
= 100 - 0.5 × 3 × 8
= 100 - 12
= 88 sq. cm. (Answer)
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Answer: (A) 88 cm^2
Step-by-step explanation:
As the side of each square is 10cm, the base of the triangle above the overlap = 4cm + 4cm = 8cm
Therefore, area of the triangle above the overlap
= 1/2 * 8 * 3 = 12cm^2
Hence, the area of the overlap
= Area of the square - area of the triangle above the overlap
= 100cm^2 - 12cm^2
= 88cm^2
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