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Question Video: Finding the Area of a Composite Shape of a Quarter Circle and a Triangle Mathematics • 7th Grade

Using 3.14 as an estimate for πœ‹, find the area of this shape.


Video Transcript

Using 3.14 as an estimate for πœ‹, 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 πœ‹π‘Ÿ squared. So therefore, the area of a quarter circle would be a quarter of this, which is πœ‹π‘Ÿ squared over four. Substituting in the value of 14 for the radius, we’ll then have πœ‹ times 14 squared over four. As 14 squared is 14 times 14, we’ll have 196πœ‹ over four. This simplifies to 49πœ‹. And as we were told to use 3.14 as an estimate for πœ‹, 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.

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