Find the area of the quadrilateral. 9 cm, 6 cm, 4 cm, and 5 cm.
To find the area of the quadrilateral, we can split it into two triangles and find the area of each triangle separately.
Using the lengths given, we can see that one triangle has sides of 9 cm, 6 cm, and 5 cm. We can use Heron's formula to find the area of this triangle:
s = (9 + 6 + 5) / 2 = 10
Area_tri1 = √(10(10-9)(10-6)(10-5)) = √(10*1*4*5) = √200 = 14.14 cm^2
Now for the second triangle with sides 4 cm, 6 cm, and 5 cm:
s = (4 + 6 + 5) / 2 = 7.5
Area_tri2 = √(7.5(7.5-4)(7.5-6)(7.5-5)) = √(7.5*3.5*1.5*2.5) = √82.88 = 9.10 cm^2
Finally, the total area of the quadrilateral is the sum of the areas of the two triangles:
Total Area = Area_tri1 + Area_tri2 = 14.14 + 9.10 = 23.24 cm^2
Therefore, the area of the quadrilateral is 23.24 square cm.