Note: the image below is a temporary reference image. If the author of this problem wants to finish the problem, the triangle below can be replaced with the correct reference image.

An engineer is planning to make an roof with a ${\displaystyle \displaystyle 30}$ m frame base. The angle of the slope of the roof to the base is ${\displaystyle \displaystyle \theta }$. The sloped sides are congruent. Use the information to answer items (a)-(b).

(a) Find the area of the roof.

(b) If the area of each square tile is ${\displaystyle \displaystyle 1{\text{ m}}^{2}}$, find the number of tiles and right triangle tiles necessary to fully cover the roof.

The idea of this worked example is to measure the area of a roof, as seen in plan, and then divide by ${\displaystyle \displaystyle \cos \theta }$, where ${\displaystyle \displaystyle \theta }$ is the angle of slope of the roof, to get the area of tiles needed. And then the quantity of tiles. Intention is to use a real roof's plan, where all the slopes are the same.