First you calculate the area of the triangle:
[tex]Area_{triangle} = \frac{base \cdot height}{2} = \frac{2 \cdot 3}{2} =3[/tex] square yards.
For the base and the height of the triangle you need to count how many squares it takes on the picture.
For the rectangle you need to calculate the length and the height first.
For each we are going to use the Pythagorean theorem:
[tex]Height^2 = 2^2 + 3^2[/tex]
[tex]Height =\sqrt{4+9}=3.6055513[/tex] yards
Again count the numbers of squares for the triangle in which the rectangle's height is the hypotenuse.
We do the same for the Length of the rectangle:
[tex]Length^2 = 4^2 + 6^2[/tex]
[tex]Height =\sqrt{16+36}=7.2111026[/tex] yards
Now we calculate the area of the rectangle:
[tex]Area_{rectangle} = Length \cdot Height = 3.6055513 \cdot 7.2111026 = 26[/tex] square yards.
The total material area to cover both is:
3 + 26 = 29 square yards
