Question

I’m confused on this one

Answer 1

So remember that the area of a trapezoid is $A=\frac{b_1+b_2}{2}h$ , 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: $A=\frac{30+40}{2}*5$

Firstly, combine everything on the numerator: $A=\frac{70}{2}*5$

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

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