#2**0 **

we have (9+8+7)/2=12 and (sqrt(12(12-9)(12-8)(12-7)))/8 to find the altitude and we find that the altitude is sqrt720/8=sqrt(11.25) then we can use the pythagorean's theorem to have sqrt(49-11.25)=sqrt37.75 and (((8-2sqrt37.75)+8)*sqrt11.25)/2=8sqrt11.25-sqrt424.6875

jimkey17 Jul 29, 2020

#4**-1 **

Use Heron's formula to find the area of triangle ACD

12sqrt5 units squared

Use the normal area of a triangle formula to get the height

12sqrt5=1/2 * 8 *h

h= 3sqrt5

units

Let X be the point such that AX is a height

Let Y be the point such that BY is a height

(SBYX is a rectangle)

since ABCD is a isosceles trapezium, DX = YC

Find YC

YC^2 = 49-45=4

YC=DX=2

XY=AB=4

\(Area=\frac{4+8}{2}*3\sqrt5\\ area=18\sqrt5 units^2\)

You need to draw the pic and check it.

I largely did it in my head so there could easily be errors.

Melody Jul 30, 2020