If the area of a triangle is 36 5/6 feet and the base of the triangle is 6 1/2 feet, what is the height?

If the area of a triangle is 36 5/6 feet and the base of the triangle is 6 1/2 feet, what is the height?

A = 36 5/6 ft²,        base (b) = 6 1/2           height (h) = ?

$${\mathtt{h}} = {\frac{{\mathtt{2}}{\mathtt{\,\times\,}}\left({\mathtt{36}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{5}}}{{\mathtt{6}}}}\right)}{\left({\mathtt{6}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right)}}$$

$${\mathtt{h}} = {\frac{\left({\mathtt{73}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}{\left({\mathtt{6}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right)}}$$

$${\mathtt{h}} = {\frac{\left({\frac{{\mathtt{442}}}{{\mathtt{6}}}}\right)}{\left({\frac{{\mathtt{39}}}{{\mathtt{6}}}}\right)}}$$

$${\mathtt{h}} = {\frac{{\mathtt{2\,652}}}{{\mathtt{234}}}} \Rightarrow {\mathtt{h}} = {\mathtt{11.333\: \!333\: \!333\: \!333\: \!333\: \!3}}$$

h = 11 1/3 ft

A = (1/2)bh   ...  so.....

36 + 5/6 =  (1/2)(6 + 1/2) h       and 36 + 5/6 =  221/6   and 6 + 1/2  =  13/2   ...so.....

221/6  = (1/2)(13/2) h

221/6  = (13/4) h     multiply both sides by 4/13

(221/6)(4/13)  = h

(221/13)(4/6)  = h

(221/13)(2/3)  = 442 / 39  = 34/3 ft  = h = (11 + 1/3) ft