Video: Finding the Area of a Composite Figure Involving a Triangle and a Semicircle

Find the area of the given figure to the nearest tenth.

02:42

Video Transcript

Find the area of the given figure to the nearest tenth.

In order to find the area or the amount of space that this shape takes up, we need to identify the component parts of this figure. We have in fact got a semicircle and a triangle. In order to find the area of a semicircle, we’ll need to recall the formula for the area of a circle. And that is that the area of a circle is equal to 𝜋 times the radius squared. Remember that it’s just the radius that’s squared and not the 𝜋 as well. As a semicircle is half of a circle, then the formula will be 𝜋𝑟 squared over two. The radius of a circle is the distance from the center to the outside edge, and that’s given to us on the diagram as 11 centimeters.

Plugging the value 𝑟 equals 11 into our formula, we’ll calculate 𝜋 times 11 squared over two. As 11 squared is 121, we’ll have 121𝜋 over two. As we’re working with an area, the units will be squared centimeters. As we’re asked to calculate our values to the nearest tenth, we can assume that we can use a calculator in this question. So we could go ahead and find the decimal value of this area. However, as we’ve not finished with this calculation, it’s sometimes easier to leave it in this format.

Let’s now find the area of the triangle. And to do this, we’ll need to recall the formula for the area of a triangle. And this is that the area of a triangle is equal to half times the base times the height. We could also write this as the base times the height over two. We need to be careful here as the base of the triangle isn’t just 11 centimeters. We’ll also need to add on 11 centimeters. We know that these two lengths are equal as they’ll both be the radii of the circle. Adding these values would give us a base of 22, and the height will be 16 centimeters. So our calculation is a half times 22 times 16. This calculation will simplify to 11 times 16, which is 176 square centimeters.

So now that we found the area of our semicircle and we found the area of our triangle, to find the total area, we add those together. We can use our calculator at this point to find that our total area is 366.06835 and so on. We’re asked to give our answer to the nearest tenth, which means that we check our second decimal digit to see if it’s five or more. And as it is, then we round our answer up to give our final answer for the area of the figure as 366.1 square centimeters.

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