Need Help with Geometry- Area of triangles, parallelograms, etc.?

Question

I need help with the following problems in my picture. If you could give me the answer and also a little summary about how you got that answer that would be most helpful. Please help me with all the problems not just one. Thanks.

http://s37.photobucket.com/albums/e82/cmartinfs/?action=view¤t=part1mathtest.jpg
In order to see my picture you must click the link. When it opens look to the left of the page and click FULL SIZE. Thanks.

Answer 1

Ok, in the first picture we have triangle, but as you can see we have the value of one side and it's altitude :

The values are : 16 cm of one side

And the value of the altitude : 7 cm

Then the area will be : 16*7 / 2 = 56 cm^2

For the second picture we have a trapezoid :

To calculate the area, we need both of the bases and the value of the altitude, from the picture, the upper base is equal to : 8 cm

We can find the lenght of the other base, just draw an altitude, and you will find a right triangle with 45º. The hypotenuse of that triangle is equal to : 5*sqrt(2). Then the altitude will be equal to : 5, because the angle is 45º

Then the other side of the triangle is equal to 5, because the right triangle is : 45 - 90 - 45.

Then the lenght of the other base will be : 8 + 5 = 13

the altitude = 5

the area of a trapezoid : (13 + 8) / 2 * 5 = 52.5

3) The other shape is a paralellogram, now, you need the value of one base and the altitude. You have a triangle inside the parallelogram, so you know that the sides of a parallelogram are parallel. So :

120º, you can move that angle to the other side, where the triangle is, and you will find out, that the value of the angle of the triangle is 60º

You have a right triangle of 90 - 60 and 30 º.

The value of the altitude of the triangle is : 5*sqrt(3)

The value of the other side of the triangle is : 5

then the area will be : area = (5+12)*5*sqrt(3) = 85*sqrt(3)

4) The last one is an equilateral triangle, so the value of the area for this triangle is :

Area = L^2*sqrt(3) / 4 >>> where "L" : lenght of the side

Area = 25*sqrt(3) / 4

That's it

Answer 2

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Answer 3

It's better to post your question one by one. Otherwise, it looks like you want someone else to do homework for you.

1.
A
= (1/2)bh
= (1/2)(16)(7)
= 56 units^2

2.
A
=(1/2)(b1+b2)h
= (1/2)(8+8+5)(5)
= 52.5 units^2

3.
A
= bh
= (12+5)5sqrt(3)
= 147.224 units^2

4.
A
= (1/2)bh
= (1/2)(5)(5/2)sqrt(3)
= 2.165 units^2