Use the image to answer the question.

A composite shape is drawn using a rectangle and a triangle. The rectangle has a base labeled as 6 centimeters. A triangle showing a perpendicular height of 6 centimeters is stacked on the top side of the rectangle. The base of the triangle and the top of the rectangle have a common side. Right angle symbols are shown on all four corners of the rectangle.

1 answer

Based on your description, we can analyze the composite shape, which consists of a rectangle with a base of 6 centimeters and a triangle on top of this rectangle that has a height of 6 centimeters.

  1. Area of the Rectangle: The area of a rectangle is calculated using the formula: \[ \text{Area} = \text{Base} \times \text{Height} \] However, the height of the rectangle is not provided. It only states the height of the triangle. If we denote the height of the rectangle as \( h \), then the area of the rectangle would be: \[ A_{\text{rectangle}} = 6 \times h \]

  2. Area of the Triangle: The area of a triangle is calculated using the formula: \[ \text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height} \] The base of the triangle is the same as the base of the rectangle (6 centimeters), and its height is 6 centimeters. Therefore, the area of the triangle is: \[ A_{\text{triangle}} = \frac{1}{2} \times 6 \times 6 = \frac{1}{2} \times 36 = 18 \text{ square centimeters} \]

  3. Total Area of the Composite Shape: The total area of the composite shape is the sum of the areas of the rectangle and the triangle: \[ A_{\text{total}} = A_{\text{rectangle}} + A_{\text{triangle}} = (6 \times h) + 18 \]

In conclusion, to find a specific numerical value for the total area, we would need the height \( h \) of the rectangle.