Find the area of an isosceles trapezoid.
Understand the Problem
The question is asking us to find the area of an isosceles trapezoid. To do this, we typically use the formula: Area = (1/2) * (Base1 + Base2) * Height, where Base1 and Base2 are the lengths of the two parallel sides, and Height is the distance between them. We need the lengths of the bases and the height to calculate this area.
Answer
The area is calculated using the formula: $$ \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h $$
Answer for screen readers
The area of the isosceles trapezoid is given by the formula:
$$ \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h $$
Substituting the numerical values for $b_1$, $b_2$, and $h$ provides the final area in square units.
Steps to Solve
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Identify the bases and height Determine the lengths of Base1, Base2, and the height from the given information. Let’s say Base1 = $b_1$, Base2 = $b_2$, and Height = $h$.
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Plug values into the area formula Use the area formula for a trapezoid: $$ \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h $$
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Calculate the sum of bases Add the lengths of Base1 and Base2: $$ \text{Sum of bases} = b_1 + b_2 $$
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Multiply by height and multiply by 1/2 Multiply the sum of the bases by the height, and then by $\frac{1}{2}$: $$ \text{Area} = \frac{1}{2} \times \text{Sum of bases} \times h $$
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Find the final area Complete the calculation to find the area. Ensure you have performed the arithmetic correctly.
The area of the isosceles trapezoid is given by the formula:
$$ \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h $$
Substituting the numerical values for $b_1$, $b_2$, and $h$ provides the final area in square units.
More Information
The area formula for a trapezoid is derived from dividing the trapezoid into a rectangle and two triangles, making it easier to visualize and calculate. Isosceles trapezoids have symmetrical properties that can make some calculations easier.
Tips
- Forgetting to divide by 2 in the area formula.
- Mixing up the lengths of the bases or height.
- Not ensuring that the units are consistent across all measurements.
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