Find the area of each of the following figures.
Understand the Problem
The question is asking to calculate the area of specific geometric figures presented in the image, which include dimensions provided for each figure.
Answer
The area is \( 55 \text{ cm}^2 \).
Answer for screen readers
The area of the figure is ( 55 \text{ cm}^2 ).
Steps to Solve
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Identify the shape and dimensions The first figure appears to be an irregular trapezoid. The dimensions given are 11 cm (height), 5 cm (top base), and 5 cm (bottom base). The longer side is indicated as 4 cm.
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Use the area formula for a trapezoid The area ( A ) of a trapezoid can be calculated using the formula: $$ A = \frac{(b_1 + b_2) \cdot h}{2} $$ where ( b_1 ) and ( b_2 ) are the lengths of the two bases, and ( h ) is the height.
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Plug in the values Here, ( b_1 = 5 \text{ cm} ), ( b_2 = 5 \text{ cm} ), and ( h = 11 \text{ cm} ). Plugging these into the formula, we get: $$ A = \frac{(5 + 5) \cdot 11}{2} $$
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Calculate the area Now calculate: $$ A = \frac{10 \cdot 11}{2} = \frac{110}{2} = 55 \text{ cm}^2 $$
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Conclusion Thus, the area of the trapezoid is ( 55 \text{ cm}^2 ).
The area of the figure is ( 55 \text{ cm}^2 ).
More Information
The area calculation utilizes the formula for the trapezoid, which is applicable to any two parallel sides height. Knowing how to derive and apply this formula is essential in geometry for area calculations.
Tips
- Forgetting to correctly identify the bases of the trapezoid or mislabeling their lengths can lead to errors in calculation.
- Not using the correct height for the calculation could also result in an incorrect area.
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