Question

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Answer 1

All? D:

Answer 2

wow... that's a lot... try one at a time... maybe you'll get hints on a problem for you to do the others yourself...

Answer 3

What do u do in class?

Answer 4

This is my first time on this site. I will try to help you with number 1 - Find the area of the trapezoid.

There a few different ways to approach this. You could decide to treat the trapezoid as three individual shapes (1 rectangle and 2 triangles) and then calculate the area of each of the three component shapes and sum them together. Or, you could simply apply the formula for finding the area of a trapezoid and input the appropriate numbers. Let's choose this second option:

Area of trapezoid=\[1/2 (b1 + b2) \times h\]
This means that you add the length of the two bases (in the diagram the bases are the top and the bottom because these are the two parallel sides) together, divide that by 2, and then multiply this result by the height of the trapezoid (the height is the distance between the bases).

First, we need to determine which numbers to use for which variables in the formula. In other words, we need to do the following:
Find b1 (base 1);
Find b2 (base 2);
Find h (height).

Notice that in the diagram the length of one of the bases is simply given to us, 7cm. And the height is also given, 5cm. Therefore, the only remaining variable to solve for is the other base, let's call it b2.

Notice that we can divide b2 (the bottom on the trapezoid in the diagram) into three component line segments. The length of right-most piece is already given to us, 5cm. Since we are told that the two dotted lines in the diagram are perpendicular to (form right angles with) the top and bottom (b1 and b2) we can transfer the length of the top (7cm) to the length of the middle segment of the bottom. Now we only need to find the length of the left-most piece of the bottom in order to know the length of the entire b2.

Looking at the left side of the trapezoid, we can see a triangle with interior angles of 45degs, 45degs, and 90degs (deg=degrees) [Note that the three interior angles of all triangles must sum to 180degs, that is why we know that the top angle in the diagram is also 45degs]. Because this triangle as two angles that are the same, we can conclude that it is an isosceles triangle, and therefore it also has two sides that are the same. Now we can determine that the length of the left-most segment of b2 is 5cm. Study the diagram and reread this paragraph to make sure you can follow my logic. I promise that it is correct.

Now we simply add the three individual pieces of b2 together:
b2= 5cm + 7cm + 5cm
b2=17cm

Now we know everything that we need: b1=7cm, b2=17cm, and h=5cm

Insert these values into the formula and we get Area =:
\[1/2 (7cm + 17cm) \times 5cm\]
simplifying this we get Area =:
\[1/2 \times 24cm \times5cm\]
simplifying more, Area =:
\[12cm \times 5cm\]
And finally:
Area = 60cm^2 [Note that cm^2 means square centimeters]

That's it! Let me know if I can help by further explaining any of the steps involved.

Peace out.

Answer 5

Hope it all makes sense.