How does one find the perimeter and the area of a cross section?

Question

Image: https://i.imgur.com/8iNniKl.png

 

A mason uses a concrete saw to cut the block along the indicated diagonal.

 

A) Find the perimeter and area of the cross section formed by the cut.

Answer 1

The cross section formed by the cut will be a rectangle.

The perimeter of the rectangle will be its width + width + height + height, or 2*(width + height)

We know the height is 215mm, but width is a bit tricky.

If we look closely, we can see that the width is the diagonal of the top face, which is also a rectangle.

Since rectangle has 4 angles of 90 degrees, we know that the diagonal will separate the top face into 2 RIGHT triangles.

We know the width of the top face, and we also know the length of the top face, so we can use Pythagorean to find out the length of the diagonal.

440^2 + 100^2 = diagonal ^2

diagonal = sqrt(440^2 + 100^2)

The perimeter of the cross section is then 2 * (215 + diagonal), and the area is diagonal * 215.