Question

I’m confused on this one

Answer 1

So remember that the area of a trapezoid is
`A=(b_1+b_2)/(2)h` , with b = bases and h = height. Before we can do the equation, however, we have to find the height. Using the right triangle, we can use the pythagorean theorem, which is
`leg^2+leg^2=hypotenuse^2` .

Since we know that the hypotenuse is 13 and one of the legs is 12, we can solve for the other leg. Our equation will look like this:
`x^2+12^2=13^2`

Firstly, solve the exponents:
`x^2+144=169`

Next, subtract 144 on both sides:
`x^2=25`

Next, square root both sides, and your height will be: x = 5

Now that we know both the height, 5, and the bases, 30 and 40, we can solve for the area of the trapezoid. Our equation will look like this:
`A=(30+40)/(2)*5`

Firstly, combine everything on the numerator:
`A=(70)/(2)*5`

Next, divide the fraction:
`A=35*5`

Next, multiply, and your answer will be A = 175 un^2.