Find the area of the trapezoid.
Area of a trapezoid: [tex]A=[?] cm^2[/tex]
[tex]\frac{\left(b_1+b_2\right)}{2} \cdot h[/tex]
Answer (2)
Identify the lengths of the bases ( b 1 = 6 cm, b 2 = 4 cm) and the height ( h = 3 cm) from the trapezoid.
Substitute the values into the area formula: A = 2 ( b 1 + b 2 ) ⋅ h = 2 ( 6 + 4 ) ⋅ 3 .
Calculate the area: A = 2 10 ⋅ 3 = 5 ⋅ 3 = 15 .
State the final answer: 15 cm 2 .
Explanation
Problem Analysis and Data Identification Let's analyze the given problem. We are asked to find the area of a trapezoid. The formula for the area of a trapezoid is given as:
A = 2 ( b 1 + b 2 ) ⋅ h
where b 1 and b 2 are the lengths of the parallel sides (bases) and h is the height (the perpendicular distance between the bases).
From the diagram, we can identify the lengths of the bases and the height. Let's assume that:
b 1 = 6 cm b 2 = 4 cm h = 3 cm
Substitute Values into Formula Now, we will substitute the values of b 1 , b 2 , and h into the formula for the area of a trapezoid:
A = 2 ( 6 + 4 ) ⋅ 3
Calculate the Area Next, we perform the calculation step by step:
First, add the lengths of the bases:
6 + 4 = 10
Then, divide the sum by 2:
2 10 = 5
Finally, multiply the result by the height:
5 ⋅ 3 = 15
So, the area of the trapezoid is 15 c m 2 .
State the Final Answer Therefore, the area of the trapezoid is 15 c m 2 .
A = 15 cm 2
Examples
Trapezoids are commonly found in architecture and engineering, such as in the design of bridges, roofs, and buildings. Calculating the area of trapezoidal shapes is essential for determining the amount of material needed for construction, estimating costs, and ensuring structural stability. For example, if you're designing a roof with a trapezoidal cross-section, knowing the area helps you calculate the amount of roofing material required, which directly impacts the project's budget and resource planning.
The area of the trapezoid is calculated using the formula A = 2 ( b 1 + b 2 ) ⋅ h . By substituting the base lengths and height into this formula, we find that the area is 15 cm 2 .
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