To find the height of the rectangle, we can first represent the areas of both the rectangle and the triangle and then set up an equation based on the total area.
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Area of the Rectangle: The area \( A \) of a rectangle is given by the formula: \[ A = \text{base} \times \text{height} \] We know the base \( b = 6 \) cm and the height \( h \) is what we need to find. So, the area of the rectangle is: \[ A_{\text{rectangle}} = 6 \times h \]
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Area of the Triangle: The area \( A \) of a triangle is given by the formula: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \] The base of the triangle is also 6 cm (same as the rectangle) and the height of the triangle is 6 cm. Thus, the area is: \[ A_{\text{triangle}} = \frac{1}{2} \times 6 \times 6 = \frac{1}{2} \times 36 = 18 \text{ cm}^2 \]
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Total Area of Composite Shape: The total area of the composite shape is given as 78 square centimeters. Therefore: \[ A_{\text{rectangle}} + A_{\text{triangle}} = 78 \] Substituting the areas we found: \[ 6h + 18 = 78 \]
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Solving for the Height of the Rectangle: Rearranging the equation to solve for \( h \): \[ 6h = 78 - 18 \] \[ 6h = 60 \] \[ h = \frac{60}{6} = 10 \text{ cm} \]
Thus, the height of the rectangle is 10 centimeters.
The correct response is:
- 10 centimeters.
1 answer