Find the area of the shaded region.

Question

Quizplus · Accepted Answer

We can see that the shaded region is a trapezoid with bases S1B1 and U1B0 and height S1U1. 
The length of S1B1 can be found using the Pythagorean theorem: 
S1B1^2 = S1U1^2 - B1U1^2 
S1B1^2 = 7^2 - 4^2 
S1B1^2 = 33 
S1B1 = sqrt(33)

The length of U1B0 can also be found using the Pythagorean theorem: 
U1B0^2 = U1S1^2 - S1B0^2 
U1B0^2 = 5^2 - 3^2 
U1B0^2 = 16 
U1B0 = 4

Now we can use the formula for the area of a trapezoid to find the area of the shaded region: 
Area = (S1B1 + U1B0) * S1U1 / 2 
Area = (sqrt(33) + 4) * 7 / 2 
Area = 55.26

Rounding to the nearest whole number, we get 55. 
Therefore, the correct answer is B) 11eaa3e5_5591_861f_9f8f_219b7f0dea8f_TB5971_11.

Find the Area of the Shaded Region