For this case we have:
Question 1:
According to Heron's formula, the area of a triangle is given by:
Where a, b and c are the sides of the triangle and s is the semi-perimeter of the triangle given by:
Let:
We have s:
Substituting in the formula of the area:
Thus, the area of the triangle is 
Answer:
Question 2:
The area of a traingule can be expressed as:
Where:
b: Base of the triangle
h: Triangle height
Let:
Substituting the values in the expression we have:
Thus, the area of the triangle is 
Answer:
Question 3:
It is known that the area of a rectangle is given by:
Where:
l: It is the length of the rectangle
w: It is the width of the rectangle
So:
Substituting:
Thus, the area of Laura's carpet is given by 
Answer:
Question 4:
We must take out the area of the outer wall, given by a rectangle, then:
Where:
l: It is the length of the rectangle
a: It is the height of the rectangle
We have:
Substituting in the formula we have:
Thus, the area of the exterior wall is given by: 
So, a can of paint is not enough to cover the exterior wall.
Answer:
A can of paint is not enough to cover the exterior wall.
Question 5:
A regular hexagon is formed by 6 equal triangles. The area of the hexagon is given by:
Where the perimeter is given by the sum of the sides, that is:
And the apothem is the height of each of the triangles that make up the hexagon, that is:
Substituting in the formula:
Thus, the area of the hexagon is 
Answer:
