All sides are different. Top is 4 cm. Right side is 6cm left side is 9cm. Bottom is 5 cm. It makes a point with perpendicular dotted line straight across. Find the area of the quadrilaterals

Answer 1

To find the area of the quadrilateral, we first need to find the height of the quadrilateral. The perpendicular line drawn from the top to the bottom of the quadrilateral divides it into two right triangles.

Using the Pythagorean theorem, we can find the height of the quadrilateral:
\(height^2 = 6^2 - 4^2 = 36 - 16 = 20\)
\(height = \sqrt{20} = 2\sqrt{5}\)

Now, we can find the area of the quadrilateral by summing the areas of the two right triangles:
\(Area = \frac{1}{2} \times 4 \times 2\sqrt{5} + \frac{1}{2} \times 5 \times 2\sqrt{5}\)
\(Area = 4\sqrt{5} + 5\sqrt{5}\)
\(Area = 9\sqrt{5} cm^2\)