Brayden was building a model car that he got for his birthday. One of the pieces is shown below.
A square shape has a piece missing from the top right corner. The piece missing looks like a quarter of a circle. The square’s sides are 20 cm long, except for the top and right side, which has part of the shape missing. Those sides are 10 cm long.
What is the area of the piece?
Brayden was building a model car that he got for his birthday. One of the pieces is shown below.
A square shape has a piece missing from the top right corner. The piece missing looks like a quarter of a circle. The square’s sides are 20 cm long, except for the top and right side, which has part of the shape missing. Those sides are 10 cm long.
What is the area of the piece?
86 cm2
78.5 cm2
321.50 cm2
314 cm2
To find the area of the missing piece, we need to calculate the area of the quarter circle and subtract it from the area of the square.
The area of the quarter circle can be found using the formula: A = (π * r^2) / 4, where r is the radius.
Since the side length of the square is 10 cm, the radius of the quarter circle is half of that, which is 5 cm.
Plugging this value into the formula, we get: A = (π * 5^2) / 4 = (π * 25) / 4.
The area of the quarter circle is therefore (π * 25) / 4.
The area of the square is simply the side length squared, which is 20^2 = 400 cm^2.
Subtracting the area of the quarter circle from the area of the square, we get 400 - (π * 25) / 4.
To calculate this value, we need to approximate π to a decimal value. Let's use 3.14.
Therefore, the area of the missing piece is approximately:
400 - (3.14 * 25) / 4 = 400 - 78.5 = 321.5 cm^2.
Therefore, the correct answer is 321.50 cm2.