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The trapezoid has an area of 232 square centimeters. What is the height of the trapezoid?

The trapezoid has an area of 232 square centimeters232\,\text{square centimeters}. What is the height of the trapezoid?

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Full solution

Q. The trapezoid has an area of 232 square centimeters232\,\text{square centimeters}. What is the height of the trapezoid?
  1. Identify Formula: Identify the formula for the area of a trapezoid.\newlineArea=12×(Base1+Base2)×Height\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}\newlineWe need to find the height, so we rearrange the formula to solve for Height.\newlineHeight=2×AreaBase1+Base2\text{Height} = \frac{2 \times \text{Area}}{\text{Base}_1 + \text{Base}_2}
  2. Substitute Values: Substitute the known values into the formula.\newlineAssuming Base1=10 cm\text{Base}_1 = 10\,\text{cm} and Base2=14 cm\text{Base}_2 = 14\,\text{cm}, and Area=232 cm2\text{Area} = 232\,\text{cm}^2,\newlineHeight=2×23210+14\text{Height} = \frac{2 \times 232}{10 + 14}
  3. Calculate Height: Calculate the height.\newlineHeight = (464)/(24)(464) / (24)\newlineHeight = 19.3319.33 cm

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