Video Transcript
A triangle has base 11 and height
11. A square has diagonal 17. What is the difference in their
areas?
To answer this question, we first
need to find the area of each shape individually. And we may find it helpful to
sketch them. The triangle has a base of length
11 units, and its height is the same.
The area of a triangle is found
using the formula a half base times height. Substituting 11 for both the base
and the height gives that the area of this triangle is a half multiplied by 11
multiplied by 11, which is 121 over two.
Next, we consider the square, which
we’re told has a diagonal of length 17 units. So, the distance between opposite
corners of the square is 17. We can calculate the area of a
square using the length of its diagonal by applying the formula area equals a half
𝑑 squared, where 𝑑 represents the length of the diagonal. This is a special case of the
general formula for finding the area of a rhombus using the lengths of its
diagonals. Substituting 17 for 𝑑 gives that
the area of the square is a half multiplied by 17 squared, which is 289 over
two.
Finally, we need to calculate the
difference in areas. So we subtract the smaller area,
that’s the area of the triangle, from the larger area, which is the area of the
square. 289 over two minus 121 over two is
168 over two, which simplifies to 84. The difference between the areas of
the square and the triangle is 84 square units.
