To find the area of the composite shape in the image, we will separate it into two right triangles.

Step-by-Step Solution:

1. Identify the two triangles:

   • The shape is divided into two right triangles by the vertical line that is 5 m above the base. Let's call the larger triangle "Triangle A" and the smaller one above it "Triangle B."

2. Dimensions of Triangle A (Larger Triangle):

   • Base: $32 \, \text{m}$
   • Height: $15 \, \text{m}$ (since the vertical distance from the base to the vertex of Triangle A is 15 m)

   The area $A_A$ of Triangle A can be calculated using the formula for the area of a triangle: $A_A = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 32 \times 15$

   $A_A = 16 \times 15 = 240 \, \text{m}^2$

3. Dimensions of Triangle B (Smaller Triangle):

   • Base: $20 \, \text{m}$
   • Height: $5 \, \text{m}$ (the vertical distance given is 5 m above the height of 15 m)

   The area $A_B$ of Triangle B can be calculated similarly: $A_B = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 20 \times 5$

   $A_B = 10 \times 5 = 50 \, \text{m}^2$

4. Calculate the total area of the composite shape: $\text{Total Area} = A_A + A_B = 240 + 50 = 290 \, \text{m}^2$

Conclusion:

The area of the composite shape is 290 square meters.

Would you like more details or have any questions?

Related Questions:

1. How would you calculate the perimeter of the composite shape?
2. How do the dimensions affect the total area of each triangle?
3. How can you confirm that the two triangles are right triangles?
4. How do you find the centroid of the composite shape?
5. How would the area change if the dimensions of the triangles were doubled?

Tip:

When dividing a composite shape into simpler shapes, ensure each shape's area can be calculated with the provided dimensions. This approach simplifies complex geometry problems.