https://file.aiquickdraw.com/mathbot/file/172748950628058ubmjj1.jpg

The diagram appears to show a composite shape consisting of a large isosceles triangle with a smaller rectangular cut-out at the base. The relevant dimensions provided are:

- The base of the large triangle is \( 14 \, \text{cm} \),
- The height of the large triangle (excluding the cut-out) is \( 5 \, \text{cm} \) (3 cm + 2 cm),
- The cut-out is a rectangle with a width of \( 2 \, \text{cm} \) and height \( 2 \, \text{cm} \).

### To find the area of the composite shape:
1. **Area of the large triangle (without cut-out):**
   - Base = \( 14 \, \text{cm} \),
   - Height = \( 5 \, \text{cm} \),
   - Area of triangle = \( \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 14 \times 5 = 35 \, \text{cm}^2 \).

2. **Area of the cut-out rectangle:**
   - Width = \( 2 \, \text{cm} \),
   - Height = \( 2 \, \text{cm} \),
   - Area of rectangle = \( 2 \times 2 = 4 \, \text{cm}^2 \).

3. **Area of the composite shape:**
   - Subtract the area of the cut-out from the area of the large triangle,
   \[
   \text{Area of composite shape} = 35 - 4 = 31 \, \text{cm}^2.
   \]

Thus, the area of the composite shape is \( 31 \, \text{cm}^2 \).

Would you like more details on this solution or have any questions?

Here are some related questions:
1. How would the area change if the cut-out was a different shape?
2. Can you calculate the perimeter of this composite shape?
3. What is the effect of doubling the dimensions of the triangle on the total area?
4. How would you find the centroid of this composite shape?
5. What happens to the area if the height of the triangle is increased?

**Tip:** For composite shapes, always break them down into simpler shapes (like triangles and rectangles) to find the area or perimeter.

Find the area of the composite shape consisting of a large isosceles triangle with a smaller rectangular cut-out at the base. The base of the large triangle is 14 cm, the height of the large triangle is 5 cm, and the cut-out has a width of 2 cm and height of 2 cm.

Learn how to calculate the area of a composite shape, which includes a large isosceles triangle and a rectangular cut-out. The triangle has a base of 14 cm and height of 5 cm, while the cut-out has dimensions of 2 cm by 2 cm. Suitable for Grades 5-7.

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