Once he chooses his structure, he needs to sketch the figure and label the whole number dimensions needed to find the surface area of the figure. His friend, Miguel, needs to build the same figure, but needs to double all of the dimensions.
Write an explanation of what happens to the surface area of the figures when the dimensions are doubled. Include all relevant math work to help clarify your explanation. please make it look like a seventh grader made the math and stuff to please
When Miguel doubles all of the dimensions of the figure that his friend chose, the surface area of the figure will also double. This is because surface area is calculated by finding the sum of the areas of all the shapes that make up the figure's surface.
For example, if the original figure has a base that is 4 units long and 2 units wide, the surface area of the figure would be 2(4)(2) + 2(4)(h) + 2(2)(h), where h represents the height of the figure. This simplifies to 16 + 8h + 4h = 16 + 12h.
When Miguel doubles all of the dimensions, the new dimensions would be 8 units long and 4 units wide. The surface area of the new figure would be 2(8)(4) + 2(8)(2h) + 2(4)(2h) = 64 + 32h + 16h = 64 + 48h.
Comparing the original surface area of 16 + 12h to the new surface area of 64 + 48h, we see that the new surface area is indeed double the original surface area when all dimensions are doubled.