MATH SOLVE

3 months ago

Q:
# help please ill mark you as brain!!!!!

Accepted Solution

A:

1. Well, first of all, let us define what we are trying to find. The surface area of the figure is the total area of its exterior surfaces - in our case, the figure is composed of a right pyramid (green shape) and a rectangular prism (blue shape).2. Now, let's start with the right pyramid. There are three parts: the right triangles (front and back), the rectangle (right) and the other rectangle (left). Whilst the bottom rectangle of the right pyramid is on top of the rectangular prism and would not be counted when calculating surface area, we should calculate its area so that we can later subtract this from the area of the top rectangle of the rectangular prism. Thus:a) Area of right triangle = (1/2)bh, where b is the base length and h is the height of the triangle. In our case, b = 5 and h = 5.Area of right triangle = (1/2)*5*5 = 12.5 cm^2Since there is one right triangle at the front and one at the back, we need to multiply this value by 2:Area = 12.5*2 = 25 cm^2b) Area of rectangle = lw, where l is the length and w is the width of the rectangle. In the case of the rectangle on the right, l = 7 and w = 4.Area of rectangle = 7*4 = 28 cm^2c) Area of rectangle = lw. In the case of the rectangle on the left, l = 5 and w = 4.Area of rectangle = 5*4 = 20 cm^2d) Area of rectangle = lw. In the case of the rectangle on the bottom (remember, this will be subtracted from the surface area of the top rectangle from the rectangular prism), l = 5 and w = 4. Area of rectangle = 5*4 = 20 cm^2Thus, the areas from a), b) and c) may be added to get:Surface area (right pyramid) = 25 + 28 + 20 = 73 cm^23. Now let's break down the rectangular prism; this is composed of six rectangles (front and back; left and right; top and bottom).i) Area of rectangle = lw. In the case of the rectangles on the front and back, l = 8 and w = 6.Area = 8*6 = 48 cm^2Since there are two rectangles, we should multiply this by 2 to get:Area = 48*2 = 96 cm^2ii) Area of rectangle = lw. In the case of the rectangles on the right and left side, l = 10 and w = 6.Area = 10*6 = 60 cm^2Again, since there are two such rectangles, we should multiply this value by 2:Area = 60*2 = 120 cm^2iii) Area of rectangle = lw. In the case of the top and bottom rectangles, l = 10 and w = 8.Area = 10*8 = 80 cm^2Thus, the area of the bottom rectangle is 80 cm^2. The area of the top rectangle in the context of the problem will only include the area that is not covered by the green shape; therefor we will need to subtract the area of the bottom of the right pyramid from the area of the top of the rectangular prism. Thus:Area = 80 - 20 = 60 cm^2If we add the areas of the top and bottom rectangles, we get:Area = 80 + 60 = 140 cm^2Now, if we add the areas we calculated in i), ii) and iii), we get:Surface area of rectangular prism = 96 + 120 + 140 = 356 cm^24. We are at the final step now; all that is left is for us to add the surface area of the right pyramid and the rectangular prism. Thus:Total surface area = 73 + 356 = 429 cm^2I hope that helps but if you have any questions or comments please don't hesitate to comment below.