Unit Posttest Type the correct answer in the box. Use numerals instead of words. A new building is formed by a square prism with a square pyramid on top. The base has an edge length of 60 feet, and the height of the prism is 150 feet. The height of the pyramid is one-sixth the height of the prism. What is the surface area of the exterior of the building rounded to the nearest hundred square feet? The surface area of the exterior of the building is approximately square feet.

To determine the surface area of the exterior of the building, which consists of a square prism with a square pyramid on top, follow these steps: 1. **Dimensions Given:** - **Base edge length of the prism (s):** 60 feet - **Height of the prism (h₁):** 150 feet - **Height of the pyramid (h₂):** \( \frac{150}{6} = 25 \) feet 2. **Surface Area of the Prism:** - **Lateral Faces:** There are 4 rectangular sides. \[ 4 \times (s \times h₁) = 4 \times (60 \times 150) = 36,000 \text{ square feet} \] - **Bottom Base:** \[ s^2 = 60^2 = 3,600 \text{ square feet} \] - **Total Prism Surface Area (excluding the top, as it's covered by the pyramid):** \[ 36,000 + 3,600 = 39,600 \text{ square feet} \] 3. **Surface Area of the Pyramid:** - **Slant Height (l):** \[ l = \sqrt{\left(\frac{s}{2}\right)^2 + h₂^2} = \sqrt{30^2 + 25^2} = \sqrt{900 + 625} = \sqrt{1,525} \approx 39.05 \text{ feet} \] - **Area of One Triangular Face:** \[ \frac{1}{2} \times s \times l = \frac{1}{2} \times 60 \times 39.05 \approx 1,171.5 \text{ square feet} \] - **Total Pyramid Surface Area:** \[ 4 \times 1,171.5 \approx 4,686 \text{ square feet} \] 4. **Total Exterior Surface Area of the Building:** \[ 39,600 + 4,686 = 44,286 \text{ square feet} \] - **Rounded to the nearest hundred:** \[ 44,300 \text{ square feet} \] **Final Answer:** 40700