Question

Kevin is building a shed. He wants to cover the triangular part of the front side with wood shingles. What area of the shed will be covered with wood shingles?

Answer 1

Let's decide on the data:

denote by x - the desired value, the ratio of the area of the triangle to the total area of the canopy

A canopy, implies a hinged roof and has the shape of an elongated triangle, approximately the following form:

Accordingly, if you do not take into account the hinged part, the front triangle is half of the total area of ​​the canopy: $x = \frac{\frac 12* a*b}{\frac 12 a*b+\frac 12a*b}= \frac 12$

If you consider the canopy then:

suppose that a, b, c - are known, the area S (of the whole canopy) will depend on the length of the canopy L and be calculated by the formula:

$S = (\frac 12* a*b)+(\frac 12*a*b)+ a*L +c*L=a*b+(a+c)*L$

where L is the length of the canopy.

Accordingly, the desired value will depend on L and be calculated by the formula:

$x = \frac{\frac 12* a*b}{a*b+(a+c)*L}$