Answer:
9. [tex]\displaystyle A=\frac{B.H}{2}[/tex]
10. B = 16 ft, H = 15 ft
11. [tex]A=120\ ft^2[/tex]
Step-by-step explanation:
Area Of The Triangle
(9)
The area of a triangle of base length B and height H is
[tex]\displaystyle A=\frac{B.H}{2}[/tex]
provided the base and height are perpendicular to each other
(10)
The dimensions of the given triangle are not the ones needed to compute its area. We need to calculate the height of the triangle, and we have the hypotenuse of one of the identical right triangles. To find the height, we must apply Pythagoras's theorem:
[tex]D^2=H^2+(B/2)^2[/tex]
Note the length of one leg of the triangle is half the length of the base. We need to solve for H:
[tex]H^2=D^2-(B/2)^2[/tex]
[tex]H^2=17^2-(16/2)^2[/tex]
[tex]H^2=289-64=225[/tex]
Thus
[tex]H=\sqrt{225}[/tex]
[tex]H=15\ ft[/tex]
(11)
Now we compute the area of the triangle
[tex]\displaystyle A=\frac{16\times 15}{2}[/tex]
[tex]A=120\ ft^2[/tex]
