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# Help and check?

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I tried to do the last one but I got the perimeter = 6√2+7√3+√105 and the area=21√2+7√105. The first one I tried but I got so confused I couldn't go any farther.  Please help!

Apr 29, 2019

#1
+106539
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First one......let's get the area...first.....the easiest way to do this one is to divide the shape up into two triangles and a rectangle, thusly :

Notice that the area of the triangle on the left  = base * height  / 2  = 6 * 3  /2  = 9 units^2

And....by symmetry....the triangle on the right has the same area......and the area of the rectangle  = 4*6 = 24 units^2

So....the area  =  9 + 9 + 24  =  42 units^2

Perimeter....note that we only need to find EF because  the outer sides of the triangles are all equal

So EF   = sqrt [ (3 - 0)^2 + (7 - 4)^2 ]  = sqrt [ 9 + 9 ]  = sqrt (18)  =  sqrt (9) *sqrt (2)  = 3sqrt(2)

So....we have   4 * 3sqrt (2)  =  12 sqrt (2)  units

And the top and bottom sides of the rectangle are 4 units each

So...the perimeter  =  4 + 4 + 12sqrt (2)   =   8 + 12sqrt(2) units

Apr 29, 2019
#2
+190
+1

For the first one, the coordinates given form a Hexagon that can be split into a rectangle and 2 triangles by cutting lines from (3,7) to (3,1) and from (7,7) to (7,1). The rectangle in the middle would have width of 4 and height of 6.

Therefore the area of the rectangle would be 4 x 6 = 24.

The height of one of the two triangles is 3 and the base is 6, so the area of one of the triangles is 3 x 6/2 = 9

Then we have to do the perimeter.

The side length of one of the legs of the triangles is 3$$\sqrt2$$

3$$\sqrt2$$ x 4 (amount of legs) = 12$$\sqrt2$$

The width of the rectangle is 4, 4 x 2= 8

The total perimeter would then be 12$$\sqrt2$$ + 8

Apr 29, 2019