Grades 7-8 Video Solutions 2022-2022_7-8

Video Transcription

Question 18. The area of the intersection of a circle and a triangle is 45% of the area of their union.  The area of the triangle outside the circle is 40% of the area of their union. What percentage of the circle lies outside the triangle?  You can start off by drawing out the triangle and circle.  When dealing with percentages, it is easy to assume 100 as a base number, since it will have the percentages break down easily.  So if we assume that the area of the union is 100 units, we can progress quickly.  The first piece of information is that the area of the intersection of the circle and triangle is 45%. 45% of 100 is just 45, so we can mark it like so.  Next, we know that the area of the triangle outside the circle is 40% of the area of their union. Again, 40% goes into 100 easily, and gives us just 40.  Next, we want to calculate the remainder of the circle. To do this, we do 100-45-40, which gives us 15. So the circle will be 15 here.  We want to know what percentage of the circle lies outside the triangle.  To do this, we will have to divide the amount of the circle that is outside the triangle, 15, by the total area of the circle, which is 45 plus 15.  When we do 15 divided by 15 plus 45, we get 15 divided by 60. When we simplify this, we will get our answer, which is B, 25%.

Video Summary

The problem involves finding the percentage of a circle that lies outside a triangle given specific areas. Assuming the union of the circle and triangle is 100 units, the area of their intersection is 45 units, and the area of the triangle outside the circle is 40 units. This leaves 15 units as the area of the circle outside the triangle. To find the percentage of the circle that lies outside the triangle, divide this area (15) by the total circle area (60), which includes both the intersection and the part outside the triangle. This calculation simplifies to 25%.

Keywords

circle

triangle

intersection

percentage

geometry