1. **State the problem:** We need to find the surface area of a triangular pyramid where each face is a congruent triangle with base $7$ ft and height $0.6$ ft.
2. **Formula for the area of a triangle:**
$$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$
3. **Calculate the area of one triangular face:**
$$\text{Area} = \frac{1}{2} \times 7 \times 0.6 = \frac{1}{2} \times 4.2 = 2.1 \text{ ft}^2$$
4. **Determine the number of faces:** A triangular pyramid (tetrahedron) has 4 triangular faces.
5. **Calculate total surface area:**
$$\text{Surface Area} = 4 \times 2.1 = 8.4 \text{ ft}^2$$
6. **Check the given options:** None match $8.4$ ft², so re-examine the height given. The problem states height is $6$ ft, but the figure shows $0.6$ ft. Assuming the height is $6$ ft (likely a typo in the figure), recalculate:
$$\text{Area} = \frac{1}{2} \times 7 \times 6 = \frac{1}{2} \times 42 = 21 \text{ ft}^2$$
$$\text{Surface Area} = 4 \times 21 = 84 \text{ ft}^2$$
7. **Final answer:** The surface area of the triangular pyramid is **84 ft²**.
Triangular Pyramid Area Aef204
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