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!

Guest Apr 29, 2019

#1**+1 **

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

CPhill Apr 29, 2019

#2**+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

Oofrence Apr 29, 2019