An illustration shows rectangle extending to a triangle on the right. The top of the rectangle extends as the hypotenuse toward the bottom. The dimensions of the figure are as follows: the top is 8 centimeters, the left is 4 centimeters, and the bottom is 10 centimeters, including the side of the extended triangle.

What is the area of the figure in square centimeters?(1 point)
cm2

1 answer

To find the area of the figure, we need to calculate the area of both the rectangle and the triangle.

  1. Calculate the area of the rectangle: The formula for the area \( A \) of a rectangle is given by: \[ A = \text{length} \times \text{width} \] Here, the length of the rectangle is 10 centimeters and the height (or width) is 4 centimeters. \[ A_{\text{rectangle}} = 10 \times 4 = 40 \text{ cm}^2 \]

  2. Calculate the area of the triangle: To find the area of the triangle, we need its base and height. The base of the triangle aligns with the bottom of the rectangle, which is 10 centimeters. The height of the triangle is the same as the height of the rectangle, which is 4 centimeters. The formula for the area \( A \) of a triangle is: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \] Thus, substituting in the values we find: \[ A_{\text{triangle}} = \frac{1}{2} \times 10 \times 4 = 20 \text{ cm}^2 \]

  3. Calculate the total area of the figure: Now we can combine the areas of the rectangle and the triangle to find the total area: \[ A_{\text{total}} = A_{\text{rectangle}} + A_{\text{triangle}} = 40 + 20 = 60 \text{ cm}^2 \]

Therefore, the area of the figure is \( \boxed{60} \) square centimeters.