Question

find the approximate area of the shaded region below, consisting of a right triangle with a circle cut out of it. use 3.14 as an approximation for π.
the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
question id: m4218
options:
6,844 square meters
1,256 square meters
2,794 square meters
974 square meters

Explanation:

Step1: Calculate area of triangle

The triangle is a right triangle with legs \( 90 \, \text{m} \) each. The formula for the area of a triangle is \( \frac{1}{2} \times \text{base} \times \text{height} \). So, \( \text{Area}_{\text{triangle}} = \frac{1}{2} \times 90 \times 90 = 4050 \, \text{m}^2 \).

Step2: Calculate area of circle

The circle has a diameter of \( 40 \, \text{m} \), so the radius \( r = \frac{40}{2} = 20 \, \text{m} \). The formula for the area of a circle is \( \pi r^2 \). Using \( \pi = 3.14 \), we get \( \text{Area}_{\text{circle}} = 3.14 \times 20^2 = 3.14 \times 400 = 1256 \, \text{m}^2 \).

Step3: Subtract circle area from triangle area

The shaded area is the area of the triangle minus the area of the circle. So, \( \text{Shaded Area} = 4050 - 1256 = 2794 \, \text{m}^2 \). Wait, but the options have 2,794 (maybe a typo in the option, but the calculation gives 2794, which matches the second option's number). Wait, wait, no—wait, did I misread the triangle? Wait, the triangle: wait, the legs are 90m? Wait, no, maybe the triangle is a right triangle with legs 90m? Wait, no, maybe I made a mistake. Wait, let's recheck. Wait, the triangle: if the legs are 90m, then area is 0.59090=4050. Circle: diameter 40, radius 20, area 3.14*400=1256. 4050-1256=2794. So the shaded area is 2794, which is the second option (2,794 square meters). Wait, but the options: the second option is "2,794 square meters". So that's the answer.

Answer:

2,794 square meters (the second option)