The base length of each square-based prism in the pedestal design is 3cm less than that of the layer immediately below.
a) Write an algebraic expression for the total of the top surface areas of the three prisms used to make the pedestal.
x
x
x
2x+5
2x+5
Please help, i am so stuck.
The surface area for each square would be the side multiplied by itself, with the bottom square = x^2.
The second square's surface would be (x-3)^2.
From this, you should be able to determine how to calculate the third square's area.
Then sum these three terms.
I hope this helps. Thanks for asking.
To find the algebraic expression for the total top surface areas of the three prisms used to make the pedestal, we need to calculate the top surface area for each prism and add them together.
Let's start by finding the top surface area of each prism:
1) The top surface area of the first prism is the square of the base length, which is x.
2) The top surface area of the second prism is also x because the base length of each square-based prism in the pedestal design is 3cm less than that of the layer immediately below.
3) The top surface area of the third prism is (2x + 5) since the base length is 3cm less than the layer immediately below and adding 5 additional centimeters.
Now, let's write the algebraic expression for the total top surface areas:
Total top surface area = Surface area of prism 1 + Surface area of prism 2 + Surface area of prism 3
Total top surface area = x + x + (2x + 5)
Simplifying the expression:
Total top surface area = x + x + 2x + 5
Total top surface area = 4x + 5
Therefore, the algebraic expression for the total top surface area of the three prisms used to make the pedestal is 4x + 5.
To find the total surface area of the three prisms used to make the pedestal, we need to add up the surface area of each prism.
Let's assume the base length of the bottom square-based prism is x cm.
According to the given information, the base length of each prism is 3 cm less than the layer immediately below. So, the base length of the middle square-based prism would be (x - 3) cm, and the base length of the top square-based prism would be ((x - 3) - 3) cm, which simplifies to (x - 6) cm.
Now, let's calculate the total surface area:
Surface area of the bottom prism = x^2
Surface area of the middle prism = (x - 3)^2
Surface area of the top prism = (x - 6)^2
To find the total surface area, we add up these three surface areas:
Total surface area = x^2 + (x - 3)^2 + (x - 6)^2
We can simplify this expression further by expanding the squared terms:
Total surface area = x^2 + (x^2 - 6x + 9) + (x^2 - 12x + 36)
Now, combine like terms:
Total surface area = x^2 + x^2 + x^2 - 6x - 12x + 9 + 36
Simplifying again:
Total surface area = 3x^2 - 18x + 45
Therefore, the algebraic expression for the total surface area of the three prisms used to make the pedestal is 3x^2 - 18x + 45.