Video Transcript
A triangle has base 11 and height 11. A square has diagonal 17. What is the difference in their areas?
We recall that the area of any triangle is equal to its base multiplied by its height divided by two. In this question, we are told that both the base and height are equal to 11. This means that the area is equal to 11 multiplied by 11 divided by two. 11 multiplied by 11 is 121. Dividing this by two gives us 60.5. Therefore, the area of the triangle is 60.5. The area of any square is equal to 𝐿 squared. In this question, we are not given the length of the square. However, we are told that its diagonal is equal to 17.
The diagonal creates two right-angle triangles, which means we can use the Pythagorean theorem. This states that 𝑎 squared plus 𝑏 squared is equal to 𝑐 squared, where 𝑐 is the length of the hypotunse or longest side of the triangle. In this question, 𝐿 squared plus 𝐿 squared is equal to 17 squared. The left-hand side of the equation simplifies to two 𝐿 squared, and 17 squared is 289. We can then divide both sides of this equation by two such that 𝐿 squared is equal to 144.5. The area of the square is 144.5.
To calculate the difference in the areas, we need to subtract 60.5 from 144.5. This is equal to 84. As there are no units given in this question, the difference in the areas of the square and triangle is 84 square units.
