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What is the area in square units of the quadrilateral XYZW shown below 

 May 20, 2020
 #1
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Divide the quadrilateral into two triangles by drawing YW.

 

Triangle(ZYW):  

 

Area(ZYW)  =  ½·32·24  =  __________

 

Since triangle(ZYW) is a right triangle, we can find YW by the Pythagorean Theorem:

 

YW2  =  322  +  242   --->   YW  =  40

 

Triangle(XYW:

 

We know the values of the three sides, so we can use Heron's formula to find the area.

 

s  =  (a + b + c) / 2   --->   s  =  (32 + 24 + 40) / 2  =  48

 

Area  =  sqrt[ s · (s - a) · (s - b) · (s - c) ]

          = sqrt[ 48 · (48 - 32) · (48 - 24) · (48 - 40) ]  =  ____________

 

The area of the quadrilateral will be these two areas added together.

 May 20, 2020
 #2
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Your concept is good, but the numbers are wrongsmiley

 

Triangle XWY side lengths are  104, 96, and 40

 

Semiperimeter        s = (104+96+40) /2 = 120

 

Area                A = sqrt[ s(s-a)(s-b)(s-c)]

 

                        A = sqrt[120(120-104)(120-96)(120-40)]

Guest May 21, 2020

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