Video Transcript
Using 3.14 as an estimate for 𝜋, find
the area of this shape.
We notice that this composite figure is
made up of a triangle and a quarter circle. So to find the area of the shape, we need
to calculate the area of the triangle and the area of the quarter circle and add them
together. Beginning with the triangle, we can
recall that the area of a triangle is equal to half times the base times the height. In the triangle, we can see that we have
a length of 28.5, which we can take as the base. For the height then, as we can see that
this is part of the quarter circle with a radius of 14 centimeters, then this means that the
height of our triangle will also be 14 centimeters. So, we’ll be calculating a half times
28.5 times 14. We can simplify this calculation to 28.5
multiplied by seven, which evaluates as 199.5. And as we’re working with an area, we’ll
have the square units of square centimeters.
Next, we can find the area of the quarter
circle. And we can recall that the area of a
circle is 𝜋𝑟 squared. So therefore, the area of a quarter
circle would be a quarter of this, which is 𝜋𝑟 squared over four. Substituting in the value of 14 for the
radius, we’ll then have 𝜋 times 14 squared over four. As 14 squared is 14 times 14, we’ll have
196𝜋 over four. This simplifies to 49𝜋. And as we were told to use 3.14 as an
estimate for 𝜋, then we can evaluate 49 times 3.14 as 153.86. And our units here will still be in
square centimeters. We can now use these two areas to find
the total area. So we add the area of our triangle,
199.5, to the area of our quarter circle, which was 153.86. And so our final answer is 353.36 square
centimeters.
