Sarah is designing a triangular pyramid made of all glass to go on top of a building. All of the faces of the pyramid have a height of 17 feet and a base of 20 feet.
How much glass is needed?
First, we need to find the area of one face of the pyramid. Since it is a triangle, we can use the formula for the area of a triangle:
A = 1/2 * base * height
A = 1/2 * 20ft * 17ft
A = 170ft^2
Since there are four faces to the pyramid, we can multiply this area by 4:
4 * 170ft^2 = 680ft^2
Therefore, 680 square feet of glass is needed for the triangular pyramid.
Karina is creating two pyramids with the nets below using construction paper. In both nets, all of the triangular faces of the pyramids have a height of 9 inches and a base of 6 inches. Compare the amount of construction paper needed to make each pyramid.
Since both pyramids have the same dimensions for each triangular face, they will require the same amount of construction paper for each face. Therefore, the total amount of construction paper needed for each pyramid will depend on the number of triangular faces each pyramid has.
Looking at the nets, we can see that Pyramid A has a square base and four triangular faces, while Pyramid B has a rectangular base and four triangular faces.
Pyramid A:
- Square base with side length of 6 inches
- Four triangular faces with base of 6 inches and height of 9 inches
The area of one triangular face is:
A = 1/2 * base * height
A = 1/2 * 6in * 9in
A = 27in^2
Since there are four triangular faces, the total amount of construction paper needed for Pyramid A is:
4 * 27in^2 = 108in^2
Pyramid B:
- Rectangular base with dimensions of 6 inches by 9 inches
- Four triangular faces with base of 6 inches and height of 9 inches
The area of one triangular face is again:
A = 1/2 * base * height
A = 1/2 * 6in * 9in
A = 27in^2
Since there are four triangular faces, the total amount of construction paper needed for Pyramid B is also:
4 * 27in^2 = 108in^2
Therefore, both pyramids require the same amount of construction paper, despite having different base shapes.
1/8 divided by 2
To divide 1/8 by 2, we can use the following formula:
dividend / divisor = quotient
Where the dividend is the number being divided, the divisor is the number we are dividing by, and the quotient is the answer we get after division.
In this case, the dividend is 1/8 and the divisor is 2. So, we can plug them into the formula:
1/8 / 2 = quotient
To simplify this fraction, we can first convert the division into multiplication by taking the reciprocal of the divisor:
1/8 * 1/2 = quotient
Now, we can multiply the numerators together and the denominators together:
1 * 1 = 1
8 * 2 = 16
So, the quotient is 1/16.
Therefore, 1/8 divided by 2 is equal to 1/16.