Calculate the area of the given shape.
Understand the Problem
The question is asking for the area of the given geometric shape, which appears to be a composite figure. To solve it, we will need to calculate the area of the rectangle and the triangle, and then sum those areas together.
Answer
The area is $966 \, \text{cm}^2$.
Answer for screen readers
The area of the composite shape is $966 , \text{cm}^2$.
Steps to Solve
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Identify the Geometric Shapes The figure is a composite shape made of a rectangle and a triangle.
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Calculate the Area of the Rectangle The area ( A_{rectangle} ) can be calculated using the formula: $$ A_{rectangle} = \text{length} \times \text{width} $$ Given dimensions: length = 32 cm and height = 21 cm.
Calculating: $$ A_{rectangle} = 32 , \text{cm} \times 21 , \text{cm} = 672 , \text{cm}^2 $$
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Calculate the Area of the Triangle The triangle has a base of 28 cm (the distance at the top) and a height of 21 cm (the vertical length). The area ( A_{triangle} ) is given by the formula: $$ A_{triangle} = \frac{1}{2} \times \text{base} \times \text{height} $$ Calculating: $$ A_{triangle} = \frac{1}{2} \times 28 , \text{cm} \times 21 , \text{cm} = 294 , \text{cm}^2 $$
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Sum the Areas To get the total area ( A_{total} ): $$ A_{total} = A_{rectangle} + A_{triangle} $$ Calculating: $$ A_{total} = 672 , \text{cm}^2 + 294 , \text{cm}^2 = 966 , \text{cm}^2 $$
The area of the composite shape is $966 , \text{cm}^2$.
More Information
The area calculated includes both the rectangular and triangular portions of the composite shape. Understanding how to decompose shapes into simpler geometric figures is essential for calculating area effectively.
Tips
- Incorrectly identifying the dimensions of the rectangle or triangle.
- Forgetting to divide by 2 when calculating the area of the triangle.
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