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Math Help - Area help

  1. #1
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    Area help

    Hello guys. I need some help with 3 problems and a double check on 2 problems.
    Imageshack - 45158138.jpg

    For the trapezoid it is isosceles and the perimeter is 32. How do I find the hegiht to find the area? For some reason I keep on getting 2.5 for the height and it's wrong.

    Now the second image with the square I am totally clueless on how to get started with that one... If someone can walk me through it that would be great.

    Finally the third one is a 12 by 16 feet rectangular floor that will be covered by square tiles that are 2 feet on each side. If the tiles are not cut, how many of them will be needed to cover the floor? For this one I got 96, but it's not the right answer...

    Now for double checking.
    There are two similar trapezoids the small one has a base of 24 and an area of 558 the large trapezoid has a base of 57 what is the area? I got 1325.

    There are two similar triangles the large triangle side length measure 40 with an area of 1589 the smaller triangle has a side length of 35 what is the area? I got 1390 for this.

    Thanks for your guys help!
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  2. #2
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    1. Trapezoid: Since the perimeter is 32 and the trapezoid is isosceles, each of the other sides is (1/2)(32 - 14 - 8) = (1/2)(10) = 5. Hint: Draw altitudes from the base of length 8 to the base of length 14. What length does the base of the right triangle have?

    2. Triangle inside square: The triangle has a base of 20 and a height of 20. What is the formula for the area of a triangle?

    3. The area of the floor is 12 x 16 = 192, and the area of each tile is 2 x 2 = 4. How many tiles do you need to cover the floor, in terms of both of these areas?

    You are wrong on both of the other problems. Remember that the area varies as the square of the side length.
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  3. #3
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    Quote Originally Posted by icemanfan View Post
    1. Trapezoid: Since the perimeter is 32 and the trapezoid is isosceles, each of the other sides is (1/2)(32 - 14 - 8) = (1/2)(10) = 5. Hint: Draw altitudes from the base of length 8 to the base of length 14. What length does the base of the right triangle have?

    2. Triangle inside square: The triangle has a base of 20 and a height of 20. What is the formula for the area of a triangle?

    3. The area of the floor is 12 x 16 = 192, and the area of each tile is 2 x 2 = 4. How many tiles do you need to cover the floor, in terms of both of these areas?

    You are wrong on both of the other problems. Remember that the area varies as the square of the side length.

    WOW! Thanks for your help numbers 1 and 3 were actually pretty easy now that you explained it a little, but I still don't get number 2 I know the formula is 1/2bh.
    For the other two I don't get what you mean can you make it a little more clear if possible?
    Thanks for your help so far!
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  4. #4
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    2. You know both the base and the height of the triangle, so all you have to do is plug them into the formula.

    For the other two problems, let me explain an easier problem. Suppose you have two squares. One has a side length of 1 and the other has a side length of 3. The ratio of the sides is 3:1, but the ratio of the areas is 9:1. The same principle applies to similar triangles and trapezoids.
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  5. #5
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    Quote Originally Posted by icemanfan View Post
    2. You know both the base and the height of the triangle, so all you have to do is plug them into the formula.

    For the other two problems, let me explain an easier problem. Suppose you have two squares. One has a side length of 1 and the other has a side length of 3. The ratio of the sides is 3:1, but the ratio of the areas is 9:1. The same principle applies to similar triangles and trapezoids.
    So the area for both the shaded triangles is 200? Was it really that simple?

    For the other two I reduce the fraction then square it?
    If so is the area of the trapezoid 3147.46?
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