David and his dad were going camping. when they went into the garage to get their tent they noticed it was ripped. david’s dad said he could fix the tent. he would buy some new material to cover the one rectangular side that ripped. a) how much material does he need to cover the one rectangular side of the tent with the rip? justify your answer using equations/formulas, models, and/or words to explain your mathematical reasoning. the area of the rectangular side is x=9 times 6. so x = 54. and x always uses length times width. b) if david’s dad wanted to re-cover the whole tent including the bottom, how much material would he need? justify your answer using equations/formulas, models, and/or words to explain your mathematical reasoning. i have to find the areas of each face of the tent and then add them. so first, i took the triangular sides of the tent. and i can find the area of them both, if i multiplied by 2. so my formula is ½ times 7 x 6, which equals 42. then for the rectangular sides, 2x9x6 would equal 10, so if i add those together it would need 150 square feet of tent. c) what is the volume of the tent? justify your answer using equations/formulas, models, and/or words to explain your mathematical reasoning. (you need to find the area of one of the triangular bases, and then you can take that measurement and multiply it with the height of the entire prism.) v=bh, where b = area of one of the triangular bases

A)How much material does he need to cover the one rectangular side of the tent with the rip? Justify your answer using equations/formulas, models, and/or words to explain your mathematical reasoning.  

If David’s dad wanted to cover the rectangular side of the tent, he would need to multiply the sides together. Using the formula A = l x w, I can solve for 6 and 9. 9 x 6 = 54, so 54 = 6 x 9.  

B)If David’s dad wanted to re-cover the whole tent including the bottom, how much material would he need?  Justify your answer using equations/formulas, models, and/or words to explain your mathematical reasoning.

If he wanted to re-cover the whole tent, he would need the product of the rectangular side, the triangular side, and the bottom side. Using A = l x w, I can solve for each side of the tent, For the rectangular side you multiply six by nine, then multiply two by the product. 6 x 9 = 54 x 2 = 108. For the triangular side, I need to multiply six times seven, 6 x 7 = 42. For the bottom, I need to multiply seven times nine, 7 x 9 = 63. Finally, I need to add them all up. 108 + 42 + 63 = 213 ft².                    

C)What is the volume of the tent?  Justify your answer using equations/formulas, models, and/or words to explain your mathematical reasoning. (You need to find the area of one of the triangular bases, and then you can take that measurement and multiply it with the height of the entire prism.) V=Bh, where B = area of one of the triangular bases

I need to find the volume of the tent, so I need to find the formula which is V = B x h. The base is 63, because I needed to find the area of one of the triangular bases, so I multiplied 7 x 9 = 63. The height is 6, so I need to multiply 63 x 6. When I multiply 63 x 6, I get the product of 378, so the volume of the tent is 378 ft³.

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