Each square in the grid below has area 1. find the area of the irregular quadrilateral below.

31.275 units²

Step-by-step explanation:

We'll find the total area by breaking up this given area into two separate parts, finding the area of each part separately, and then adding these two sub-areas together.

First, draw a horizontal line through the rightmost vertex, which creates a triangle of base 7.5 and height 5.  

The formula for the area of a triangle of base b and height h is A = (1/2)(b)(h).  Thus, the area of the triangle we have created is

A = (1/2)(7.5)(5) = 18.75 units²

The bottom half of the given irregular quadrilateral is a trapezoid of width 3 units.  We must use the Pythagorean Theorem twice to find the lengths of the two legs.  On the far left we have a triangle with longer side 3 and shorter side 1.5; the hypotenuse of this triangle is

√(1.5² + 3²), or √11.25.  This is the measure of the shorter leg of the trapezoid.

On the far right we have another triangle with loger leg 4 and shorter leg 3.  The length of the hypotenuse is also the length of the longer leg of the trapezoid.  It is √(3°2 + 4°) = 5.

Now we'll use the formula for the area of a trapezoid:

A = (average length of legs of trapezoid)(width of trapezoid)

        √11.25 + 5                8.35              25.06

   = * 3  = * 3 = = 12.53 units²

                 2                          2                     2

Our last step is to add together the triangle area found earlier and the trapezoid area just found here:

Total area = 18.75 units² + 12.53 units² =  31.275 units²

The total area of the irregular quadrilateral is 31.275 units²

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step-by-step explanation:

exactly you go it

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