rectangular prism with base perimeter 30 cm, base area 50 cm^2, and height 150 cm.
Choices are:
A. 7,560 cm^2
B. 4,600 cm^2
C. 1,800 cm^2
D. 4,550 cm^2
apparently you want the surface area.
for sides, perimeter*height = 4500
for bases, 2*50=100
(B)
To find the surface area of a rectangular prism, we need to calculate the sum of the areas of all its faces.
Since the base of the prism is a rectangle, which has a perimeter of 30 cm, we can divide the perimeter by 4 (since a rectangle has four sides of equal length) to find the length of each side of the base:
Perimeter = 2(Length + Width)
30 = 2(L + W)
15 = L + W
Since we know that the base area is 50 cm^2, we can use this information to create an equation for the area of the base:
Area = Length * Width
50 = L * W
Now we have a system of two equations:
15 = L + W
50 = L * W
Using these equations, we can solve for the values of L and W. Let's solve for W in terms of L:
15 - L = W
Substitute this expression for W into the area equation:
50 = L * (15 - L)
50 = 15L - L^2
Rearrange the equation:
L^2 - 15L + 50 = 0
To solve for L, we can either factor the quadratic equation or use the quadratic formula. In this case, it is easier to factor the equation:
(L - 5)(L - 10) = 0
So, L = 5 or L = 10.
If L = 5, then W = 10 - 5 = 5.
If L = 10, then W = 15 - 10 = 10.
Now that we have the values of L and W, we can calculate the surface area of the rectangular prism:
Surface Area = 2(LW + LH + WH)
= 2(5 * 5 + 5 * 150 + 5 * 150)
= 2(25 + 750 + 750)
= 2(1525)
= 3050
Therefore, the correct answer is D. 4,550 cm^2.