Question

The Louvre is an art museum in Paris. A glass square base pyramid sits in front of the entrance to the museum. If the pyramid is 40 meters wide around the square base and has a height of 21 meters, what is the minimum amount of glass needed to construct the pyramid (lateral surface area only)?
Hint: You need to calculate slant height in order to answer this question. Use Pythagorean Theorem.



The minimum amount of glass used for the lateral surface area of the Louvre pyramid is ______ m2.


3117

2320

1442

1893

Answer 1

Answer:

lateral area = 2320 m²

Step-by-step explanation:

The question wants us to calculate the lateral area of a square base pyramid. The square base pyramid has a side of 40 meters.The height is 21 meters.

Half of the square base is 40/2 =  20 meters . With the height it forms a right angle triangle. The hypotenuse side is the slant height of the pyramid.

Using Pythagoras's theorem

c² = a² + b²

c² = 20² + 21²

c² = 400 + 441

c² = 841

square root both sides

c = √841

c = 29 meters

The slant height of the pyramid is 29 meters.

The pyramid has four sided triangle. The lateral area is 4 multiply by the area of one triangle.

area of triangle = 1/2 × base × height

base = 40 meters

height = 29 meters

area = 1/2 × 40 × 29

area = 580

area of one triangle = 580 m²

Lateral area = 4(580)

lateral area = 2320 m²