1. **Problem Statement:** Find the volume and surface area of a triangular prism with base triangle dimensions base = 8 ft, height = 5 ft, prism length = 14.2 ft, and another edge 5.8 ft. 2. **Volume Formula:** The volume $V$ of a prism is given by: $$V = \text{Base Area} \times \text{Length}$$ where Base Area is the area of the triangular base. 3. **Calculate Base Area:** The area $A$ of a triangle is: $$A = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times 5 = 20 \text{ ft}^2$$ 4. **Calculate Volume:** $$V = 20 \times 14.2 = 284 \text{ ft}^3$$ This matches your volume answer, so volume is correct. 5. **Surface Area Formula:** Surface area $S$ of a prism is: $$S = 2 \times \text{Base Area} + \text{Perimeter of base} \times \text{Length}$$ 6. **Calculate Perimeter of Base Triangle:** You gave one other edge as 5.8 ft, so the triangle sides are 8 ft, 5 ft (height is not a side, so we need the third side). Assuming the triangle is right-angled with legs 8 ft and 5 ft, the hypotenuse is: $$\sqrt{8^2 + 5^2} = \sqrt{64 + 25} = \sqrt{89} \approx 9.43 \text{ ft}$$ But you mentioned 5.8 ft as another edge, so possibly the triangle is not right angled or 5.8 ft is a side of the prism (not base). For surface area, we need the perimeter of the base triangle. 7. **Assuming base triangle sides are 8 ft, 5.8 ft, and 5 ft:** $$P = 8 + 5.8 + 5 = 18.8 \text{ ft}$$ 8. **Calculate Surface Area:** $$S = 2 \times 20 + 18.8 \times 14.2 = 40 + 266.96 = 306.96 \text{ ft}^2$$ 9. **What you did wrong:** - You multiplied 5 x 14.2 x 8 = 568, which is not a correct formula for surface area. - You divided 568 by 2 to get 284, which is the volume, not surface area. - Surface area requires adding twice the base area plus the lateral area (perimeter times length), not multiplying all dimensions together. **Final answers:** - Volume = $284 \text{ ft}^3$ - Surface Area = $306.96 \text{ ft}^2$