1. **State the problem:** We need to find the surface area of a rectangular pyramid with base edges 20 cm and 36 cm, and heights 30 cm and 26 cm from the apex perpendicular to the base edges. 2. **Identify the surface area formula:** The surface area $S$ of a pyramid is the sum of the base area and the areas of the triangular faces. $$S = \text{Base Area} + \text{Lateral Area}$$ 3. **Calculate the base area:** The base is a rectangle with sides 20 cm and 36 cm. $$\text{Base Area} = 20 \times 36 = 720 \text{ cm}^2$$ 4. **Calculate the slant heights of the triangular faces:** The pyramid has two pairs of triangular faces adjacent to the base edges. - For the side with base 20 cm, the slant height is 30 cm. - For the side with base 36 cm, the slant height is 26 cm. 5. **Calculate the area of each triangular face:** The area of a triangle is $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ - Triangles with base 20 cm and slant height 30 cm: $$\frac{1}{2} \times 20 \times 30 = 300 \text{ cm}^2$$ - Triangles with base 36 cm and slant height 26 cm: $$\frac{1}{2} \times 36 \times 26 = 468 \text{ cm}^2$$ 6. **Calculate total lateral area:** There are two triangles of each type, so $$2 \times 300 + 2 \times 468 = 600 + 936 = 1536 \text{ cm}^2$$ 7. **Calculate total surface area:** $$S = 720 + 1536 = 2256 \text{ cm}^2$$ **Final answer:** The surface area of the rectangular pyramid is $2256$ cm$^2$.