What is the area of the shape with dimensions 11 cm, 14 cm, 10 cm, and 2 cm?
Understand the Problem
The question is asking for the area of a specific shape that includes dimensions provided, which indicates that it involves calculations based on geometric properties.
Answer
The area is \( 88 \, \text{cm}^2 \).
Answer for screen readers
The area is ( 88 , \text{cm}^2 ).
Steps to Solve
- Identify the Shape and Dimensions
The shape in the problem is a trapezoid (the top part is narrower). The dimensions provided are:
- The length of the top base is $11 \text{ cm}$.
- The length of the bottom base is also $11 \text{ cm}$.
- The height (the distance between the two bases) is the total height minus the two vertical segments:
$$ \text{Height} = 10 \text{ cm} - 2 \text{ cm} = 8 \text{ cm} $$
- Calculate the Area of the Trapezoid
The formula for the area (A) of a trapezoid is given by:
$$ A = \frac{1}{2} (b_1 + b_2) h $$
Where:
- ( b_1 ) is the length of the top base
- ( b_2 ) is the length of the bottom base
- ( h ) is the height
Substituting in the values:
$$ A = \frac{1}{2} (11 \text{ cm} + 11 \text{ cm}) (8 \text{ cm}) $$
- Perform the Calculation
Calculate the area step-by-step:
First, calculate the sum of the bases:
$$ b_1 + b_2 = 11 \text{ cm} + 11 \text{ cm} = 22 \text{ cm} $$
Now substitute back into the area formula:
$$ A = \frac{1}{2} (22 \text{ cm}) (8 \text{ cm}) $$
$$ A = 11 \text{ cm} \times 8 \text{ cm} = 88 \text{ cm}^2 $$
The area is ( 88 , \text{cm}^2 ).
More Information
The shape in this problem is a trapezoid, and the method used here can be applied to any trapezoid with similar dimensions. The area formula leverages averaging the lengths of the two bases multiplied by the height.
Tips
- Confusing the heights and widths of the shape. Ensure the height is measured correctly between the two bases.
- Forgetting to divide by 2 in the trapezoid area formula. This step is crucial for accuracy.
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