https://file.aiquickdraw.com/mathbot/file/172631021691597o0zhz6.jpg

To calculate the surface area of the figure, it appears to be composed of two triangles based on the given dimensions.

Let's break down the process:

1. **First Triangle (left side)**:
   - The given dimensions are 13 m, 25 m, and 21 m.
   - We can use **Heron's formula** to find the area of this triangle. The formula for the area \( A \) of a triangle with sides \( a \), \( b \), and \( c \) is:
     \[
     A = \sqrt{s(s - a)(s - b)(s - c)}
     \]
     where \( s \) is the semi-perimeter, \( s = \frac{a + b + c}{2} \).

2. **Second Triangle (right side)**:
   - The given dimensions are 16 m, 21 m (base), and the height is 10 m.
   - For this triangle, the area can be directly computed using the standard triangle area formula:
     \[
     A = \frac{1}{2} \times \text{base} \times \text{height}
     \]

### Step-by-step solution:

- First, I'll calculate the area of each triangle.The total surface area of the figure is approximately **241.45 square meters**. This is composed of:

- The area of the first triangle (with sides 13 m, 25 m, and 21 m) is approximately **136.45 square meters**.
- The area of the second triangle (with base 21 m and height 10 m) is **105.0 square meters**.

Would you like more details on how the areas were calculated, or do you have any other questions?

Here are 5 related questions:
1. How does Heron's formula work for any triangle, regardless of its type?
2. Can the Pythagorean theorem be used in any part of this figure?
3. How would the surface area change if the height of the second triangle increased?
4. What is the difference between calculating area with Heron’s formula versus using the base-height formula?
5. How can you calculate the perimeter of this shape?

**Tip:** Always remember that for triangles, if two sides and the included angle are known, you can also use the trigonometric formula to find the area.

What is the surface area of the given shape composed of two triangles with sides 13 m, 25 m, and 21 m, and 16 m, 21 m with height 10 m?

Learn how to calculate the surface area of a composite shape composed of two triangles. This includes using Heron's formula for one triangle and the standard base-height formula for the other triangle. The total surface area is approximately 241.45 square meters. Suitable for students in Grades 8-10.

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