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.
