Calculate the area of a composite shape: a rectangle with a triangle on top and a smaller rectangle cut out…

Question

Calculate the area of a composite shape: a rectangle with a triangle on top and a smaller rectangle cut out from the bottom.

ScanSolve AI Tutor · Accepted Answer

To find the area of the given shape, we can break it down into simpler geometric figures: a large rectangle, a triangle on top, and a smaller rectangle cut out from the bottom.

Identify the dimensions of the main components.
- Total width of the base = 10 cm
- Height of the main rectangular body (left side) = 8 cm
- Total height of the figure = 13 cm
- Width of the cut-out rectangle (doorway) = 4 cm
- Height of the cut-out rectangle (doorway) = 6 cm (indicated on the right side)
Calculate the area of the large rectangular base.
This rectangle has a width of 10 cm and a height of 8 cm.
$A_{\text{large rectangle}} = \text{width} \times \text{height} = 10 \text{ cm} \times 8 \text{ cm} = 80 \text{ cm}^2$
Calculate the area of the triangular top.
The base of the triangle is the same as the width of the large rectangle, which is 10 cm.
The height of the triangle is the total height minus the height of the rectangular body:
$h_{\text{triangle}} = 13 \text{ cm} - 8 \text{ cm} = 5 \text{ cm}$
The area of the triangle is:
$A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 10 \text{ cm} \times 5 \text{ cm} = 25 \text{ cm}^2$
Calculate the area of the rectangular cut-out (doorway).
This rectangle has a width of 4 cm and a height of 6 cm.
$A_{\text{cut-out}} = \text{width} \times \text{height} = 4 \text{ cm} \times 6 \text{ cm} = 24 \text{ cm}^2$
Calculate the total area of the shape.
The total area is the sum of the area of the large rectangle and the triangle, minus the area of the cut-out rectangle.
$A_{\text{total}} = A_{\text{large rectangle}} + A_{\text{triangle}} - A_{\text{cut-out}}$ $A_{\text{total}} = 80 \text{ cm}^2 + 25 \text{ cm}^2 - 24 \text{ cm}^2$ $A_{\text{total}} = 105 \text{ cm}^2 - 24 \text{ cm}^2$ $A_{\text{total}} = 81 \text{ cm}^2$
The total area of the shape is $\text{81 cm}^2$ .

Calculate the area of a composite shape: a rectangle with a triangle on top and a smaller rectangle cut out from the bottom.

Answer

Step-by-step solution

Identify the dimensions of the main components.

Calculate the area of the large rectangular base.

Calculate the area of the triangular top.

Calculate the area of the rectangular cut-out (doorway).

Calculate the total area of the shape.

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