Mathematics: You’ve decided you want to plant for your room. At gardening store, there 4 different kinds of plants (tulip fern cactus, and ficus) and 4 kinds of pots to hold the plants ( clay pot , plastic pot, metal pot, and wood pot).

You’ve decided you want to plant for your room.

slauravillalta

06.06.2021

The area of the triangle WXY is 8.49 square units.

Step-by-step explanation:

I have graphed the points in the figure attached.

The area of any triangle is

$A=\frac{1}{2} bh$

where is the height of the triangle, and is the base.

In our case the base of the triangle is WX, and the height is YZ.

Now

(WX)^2=(WY)^2+(YX)^2

and since

$WY=\sqrt{(2-7)^2+(-1-0)^2} =\sqrt{26}$

$(YX)^2=\sqrt{(7-6)^2+(0-3)^2} =\sqrt{10}$

$(WX)^2=(\sqrt{26} )^2+(\sqrt{10} )^2=36$

$\boxed{ WX=6}$

Now we find the height YZ:

$YZ=\sqrt{(7-5)^2+(0-2)^2}$

$\boxed{ YZ=2\sqrt{2}}$

Now we are ready to find the area of the triangle:

$A=\frac{1}{2}(YZ)(WX)$

$A=\frac{1}{2}*2 \sqrt{2}*6$

$\boxed{A=6\sqrt{2} }$

Which, when simplified as a decimal, is 8.49 square units.

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