## Friday, April 18, 2014

Category: Plane Geometry

"Published in Vacaville, California, USA"

A sail has a spread of canvass as shown in the figure. Find the surface area of one side of the sail.

 Photo by Math Principles in Everyday Life

Solution:

The given sail canvass is a general quadrilateral because the two opposite sides are not parallel. Because of this, we need to divide this into two triangles as follows

 Photo by Math Principles in Everyday Life

The first triangle is a right triangle because the two adjacent sides are perpendicular to each other. Consider the right triangle at the left side. The area of a first triangle is

Consider the general triangle at the right side. In order to get the value of x, use Pythagorean Theorem at the first triangle, we have

Since the other side of a second triangle is also 15 ft., then the second triangle is an isosceles triangle. Use Heron's Formula in order to get the area of the second triangle, we have

where a, b, and c are the sides of a triangle and s is the semi-perimeter of a triangle.

The perimeter of a triangle is

The semi-perimeter of a triangle is

Hence, the area of a second triangle is

Therefore, the area of a sail canvass is