Subjects geometry

Surface Area Pyramid 70E646

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1. **State the problem:** We need to find the surface area of a right rectangular pyramid with a rectangular base of sides 7 yd and 7 yd, a slant height of 6 yd for the triangular faces, and a vertical height of 4.9 yd. 2. **Formula for surface area of a right rectangular pyramid:** $$\text{Surface Area} = \text{Base Area} + \text{Lateral Area}$$ where $$\text{Base Area} = l \times w$$ and $$\text{Lateral Area} = \frac{1}{2} \times \text{Perimeter of base} \times \text{Slant height}$$ 3. **Calculate the base area:** $$7 \times 7 = 49$$ sq yd 4. **Calculate the perimeter of the base:** $$2 \times (7 + 7) = 2 \times 14 = 28$$ yd 5. **Calculate the lateral area:** $$\frac{1}{2} \times 28 \times 6 = 14 \times 6 = 84$$ sq yd 6. **Calculate total surface area:** $$49 + 84 = 133$$ sq yd 7. **Answer:** The surface area of the right rectangular pyramid is **133 sq yd**.