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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