Find the lateral area and surface area of the given prism. Round your answer to the nearest whole number.
15 in 17 in 18 in
the prism has three pairs of parallel rectangular faces, right? So the area is
2(15*17 + 15*18 _ 17*18) = _____ in^2
1. Multiple: 15 * 17 = 255
2. Multiple: 15 * 18/17= 15 · 18/1 · 17 = 270/17
3. Then multiply the result of step 2 * 18 = 270/17 * 18 = 270 · 18/17 · 1
= 4860/17
4. Add: the result of step No. 1 + the result of step No. 3 = 255 + 4860/17
= 255/1+ 4860/17 = 255 · 17/1 · 17 + 4860/17 = 4335/17 + 4860/17
= 4335 + 4860/17 = 9195/17
5.Multiple: 2 * the result of step No. 4 = 2 * 9195/17 = 2 · 9195/1 · 17
= 18390/17
Is this how to get the answer or no @oobleck?
oops - my typo
2(15*17 + 15*18 + 17*18)
= 2(255+270+306)
= 2(831)
= 1662
whatever made you think you had to do a division? It was clearly the sum of three rectangles ...
To find the lateral area and surface area of a prism, we need to determine the dimensions of the prism. From the given measurements, it seems that we have a rectangular prism with a length of 15 inches, width of 17 inches, and height of 18 inches.
1. Lateral area:
The lateral area is the combined area of all the faces of the prism except for the top and bottom faces. To find the lateral area, we need to calculate the perimeter of the base and multiply it by the height of the prism.
The perimeter of the base can be found by summing the lengths of all the sides. In this case, the base is a rectangle, so its perimeter is calculated as:
Perimeter of base = 2 * (length + width)
Plugging in the values, we have:
Perimeter of base = 2 * (15 inches + 17 inches)
= 2 * (32 inches)
= 64 inches
Now, multiply the perimeter of the base by the height to find the lateral area:
Lateral area = Perimeter of base * height
= 64 inches * 18 inches
= 1,152 square inches
Rounding to the nearest whole number, the lateral area is approximately 1,152 square inches.
2. Surface area:
The surface area of a prism includes the combined area of all its faces. To find the surface area, we need to calculate the area of each face and sum them up.
The formula for the area of a rectangle is given by:
Area of rectangle = length * width
In this case, there are two bases (top and bottom) with the dimensions 15 inches by 17 inches. Thus, the total area of both bases is:
Total base area = 2 * (15 inches * 17 inches)
= 2 * (255 square inches)
= 510 square inches
Additionally, there are four lateral faces, each with dimensions equal to the height (18 inches) multiplied by one side of the base (either the length or width). So, the total lateral area is:
Total lateral area = Perimeter of base * height
= 64 inches * 18 inches
= 1,152 square inches
Now, sum up the base area and lateral area to find the total surface area:
Surface area = Total base area + Total lateral area
= 510 square inches + 1,152 square inches
= 1,662 square inches
Rounding to the nearest whole number, the surface area is approximately 1,662 square inches.
Therefore, the lateral area of the prism is about 1,152 square inches, and the surface area is about 1,662 square inches.