Question

topic: circles
progress
question c. 18901
the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer
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.
image of a right triangle with legs 56 m and a circle inside with diameter 20 m (from the center mark?)
options:
2,822 square meters
1,254 square meters
314 square meters
312 square meters

Explanation:

Step1: Calculate triangle area

Area of triangle = $\frac{1}{2} \times 56 \times 56 = 1568$? No, wait: the triangle is right-angled with legs 56m each? Wait, no—wait, the circle has diameter 20m (radius 10m). Wait, correct: Triangle legs are 56m each. Area = $\frac{1}{2}×56×56 = 1568$? No, wait no—wait the problem says shaded area is triangle minus circle. Wait circle radius: 10m (diameter 20m). Area of circle = $\pi r^2 = 3.14×10^2 = 314$. Area of triangle: $\frac{1}{2}×56×56 = 1568$? No, wait 56×56=3136, half is 1568. 1568 - 314 = 1254? No, wait wait—wait maybe the triangle legs are 60m? No, the image shows triangle legs 56m, circle diameter 20m. Wait no, let's recalculate: Area of triangle = $\frac{1}{2}×base×height = \frac{1}{2}×56×56 = 1568$. Area of circle = $3.14×(10)^2 = 314$. Shaded area = 1568 - 314 = 1254. Oh, option B is 1,254. Wait I made a mistake earlier: 56×56=3136, half is 1568, minus 314 is 1254. So correct answer is B.

Wait correction:

Step1: Compute triangle area

Area = $\frac{1}{2}×56×56 = 1568$ m²

Step2: Compute circle area

Radius = 10m, Area = $3.14×10² = 314$ m²

Step3: Shaded area = triangle - circle

$1568 - 314 = 1254$ m²

Step1: Calculate triangle area

$\frac{1}{2}×56×56 = 1568$

Step2: Calculate circle area

$3.14×10^2 = 314$

Step3: Find shaded area

$1568 - 314 = 1254$

Answer:

A. 2,822 square meters