Answers:
Claim: Area of triangle is 34 square feet
Answer: True
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Claim: Area of parallelogram is 56 square cm
Answer: False (it's actually 63 square cm)
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Claim: Area of trapezoid is 24 square inches
Answer: True
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Explanations:
To get the area of a triangle, multiply the base and height, then divide by 2
area of triangle = base*height/2
area of triangle = 10*6.8/2
area of triangle = 68/2
area of triangle = 34 square feet
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For a parallelogram, the area is simply base times height
area = base*height
area = 9*7
area = 63
It might help to rotate the figure so that the 9 cm side is completely horizontal.
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The trapezoid formula is a bit more tricky. We basically need to average the two parallel sides, then we follow the same basic path as the parallelogram route above.
The parallel sides are 9 and 7 inches which average to (9+7)/2 = 16/2 = 8. Note how 8 is directly between 7 and 9. Multiply the result 8 with the height 3 to get 8*3 = 24.
This is what it looks like when you use the trapezoid area formula
The 0.5 inch portion is never used.