Answer :

Answer

the total area of the composite shape is approximately 31.5 square units.

Step-by-step explanation:

Let's find the area of the composite shape in the image. It consists of a triangular roof on top of a rectangular base. To calculate the area, we'll break it down into two parts: the rectangle and the triangle.

1. Rectangle (Base):

  - The base of the shape is a rectangle with dimensions:

    - Length (along the x-axis): $4 - 1 = 3$ units

    - Width (along the y-axis): $8 - 1 = 7$ units

  - Area of the rectangle: $\text{Length} \times \text{Width} = 3 \times 7 = 21$ square units.

2. Triangle (Roof):

  - The vertices of the triangle are located at coordinates (1,1), (4,1), and (2,8).

  - Base of the triangle: The distance between (1,1) and (4,1) is 3 units.

  - Height of the triangle: The distance between the base (4,1) and the top vertex (2,8) is 7 units.

  - Area of the triangle: $\frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 3 \times 7 = 10.5$ square units.

3. Total Area:

  - Sum of rectangle area and triangle area: $21 + 10.5 = 31.5$ square units.

Therefore, the total area of the composite shape is approximately 31.5 square units.