Video: Finding the Area of Circles and Rectangles

Find the area of the shaded part of this figure. Round your answer to the nearest tenth.

02:15

Video Transcript

Find the area of the shaded part of this figure. Round your answer to the nearest tenth. Here, we can see that we have a rectangle and its area will be length times width. And there are also two circles and the area of a circle is equal to πœ‹ times the radius squared. So the shaded region is the entire rectangle, except for the circles, so we take those out. So the formula that we need to use would be the area of the rectangle minus the area of the two circles, which would be equal to length times width minus two times πœ‹π‘Ÿ squared.

So we need to find the length, the width, and the radius of the circles. So the length and the width would be 38.6 times 77.2. And now we need the radii, which is the distance from the centre to an outside point on the circle. So from here to here would also be a radius as well as this one as well as this one.

And notice all of these radii together should be equal to 77.2. So that means we could solve for the π‘Ÿ, the radius. π‘Ÿ plus π‘Ÿ plus π‘Ÿ plus π‘Ÿ would be four π‘Ÿ. And now we need to divide both sides by four. That means the radius would be 19.3. So we plug that in for π‘Ÿ and now we evaluate. So we get 2979.92 minus two times πœ‹ times 372.49.

We got the 372.49 from scoring 19.3. So let’s go ahead and take that number, multiply it by πœ‹, and then multiply it by two. And that equals 2339.24, and now we subtract. When we subtract, we find that the area of the shaded part is 640.68. But it says to round to the nearest tenth, so that’s one decimal place. So we have to decide: do we keep the six a six or round it up to seven? So we look at the number to the right of it. So since eight is larger than five, it will round the six up to a seven. Therefore, the area of the shaded part of this figure would be 640.7 centimetres squared.

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