# A building has four walls that form a quadrilateral. The walls (in plan view) are given by the equations: `y=x+10,y=-x+10,y=-x/8-8,``x=16` where `-16m<=x<=16m` and `-10m<=y<=10m` .Find...

A building has four walls that form a quadrilateral. The walls (in plan view) are given by the equations: `y=x+10,y=-x+10,y=-x/8-8,``x=16` where `-16m<=x<=16m` and `-10m<=y<=10m` .Find the plan area of the building.

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### 1 Answer

Hi, zofic,

To start this, you would need to plot the diagram. The quadrilateral isn't a small one. I have attached it to this answer. I made the equations in "light purple", and I made the quadrilateral in "light green". To find the area of this, you would break it up into the triangles I drew inside the quad. And, the area of a triangle = 1/2 * b * h. You would find the area of each triangle, then add up those area; that result is the area of the quad.

So, for triangle 1, the base is 16 units long and 16 units high (remember, we would need to go to the green; I only used the brown to visualize what I did). So:

Area 1 = 1/2 * 16 * 16 = 128 square units

For triangle 2, the base is 16 and the height is 4. So:

Area 2 = 1/2 * 4 * 16 = 32 square units.

So, the total area is 128 + 32 = 160 square units.

Good luck, Zofic. I hope this helps.

Till then,

Steve