Question

Can someone help me solve this problem. Find the area of the trapezoid HOWL plotted below. Round your answer to the nearest hundredth.

Answer 1

Take into account that the area of the given trapezoid is the sum of the area of two right triangles and one square. The area of the triangles is the same, then, we have:

A = 2A1 + A2

where A1 is the area of the triangle and A2 the area of the square.

Let's calculate the area of triangle OSH, as follow:

A1 = (OS)(SH)/2

OS and SH are segments which we can calculate by using the following formula for the distance between two points with coorindates (x1,y1) and (x2,y2):

`d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`

Based on the given coordinates points for O, S and H, we have:

`\begin{gathered} OS=\sqrt[]{(-7-(-5))^2+(-1-(-2))^2}=\sqrt[]{4+1}=\sqrt[]{5} \\ SH=\sqrt[]{(-6-(-5))^2+(-2-(-4))^2}=\sqrt[]{1+4}=\sqrt[]{5} \end{gathered}`

Then, the area of triangle OSH is:

`A_1=\frac{\sqrt[]{5}\sqrt[]{5}}{2}=(5)/(2)=2.5`

Next, let's calculate the area of the square. As you can notice on the given image, the length of the sides of the square is the same that the length of the segment OS, then, we have for the area of the square:

`A_2=(\sqrt[]{5})^2=5`

Finally, let's replace the obtained values of A1 and A2 into the expression for the total area A:

A = 2(2.5) + 5 = 5 + 5

A = 10 squared units