Question

1. nikolas is constructing a skyscraper with walls made of only glass that is 350 meters (m) high and is in the shape of a rectangular pyramid.

a. what is the surface area of the skyscraper?

Explanation:

Step1: Identify target surface area

The skyscraper has glass walls, so we calculate the lateral (side) surface area (exclude the rectangular base, as it is not a glass wall). The lateral surface area is the sum of the areas of the 4 triangular faces.

Step2: Calculate area of first pair of triangles

These triangles have base $180\ \text{m}$ and slant height $357.4\ \text{m}$. Area of one triangle: $\frac{1}{2} \times 180 \times 357.4$. For two triangles:
$2 \times \frac{1}{2} \times 180 \times 357.4 = 180 \times 357.4 = 64332\ \text{m}^2$

Step3: Calculate area of second pair of triangles

These triangles have base $145\ \text{m}$ and slant height $361.4\ \text{m}$. Area of one triangle: $\frac{1}{2} \times 145 \times 361.4$. For two triangles:
$2 \times \frac{1}{2} \times 145 \times 361.4 = 145 \times 361.4 = 52403\ \text{m}^2$

Step4: Sum the two lateral areas

Add the areas from Step2 and Step3 to get total lateral surface area.
$64332 + 52403 = 116735$

Answer:

$116735\ \text{square meters}$