Question

2. Heron's Formula (Fill-in from worksheet) A = a. With the sides a = 7, b = 14 C = 15 b. With the sides a = 11, b = 12 and c = 16

Answer 1

Heron's formula for the area of a triangle is;

`\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ \text{where} \\ s=(a+b+c)/(2) \end{gathered}`

Let's compute these areas;

i. a = 7 , b = 14 , c = 15 ;

`\begin{gathered} s=(7+14+15)/(2) \\ s=18 \\ \text{thus} \\ A=\sqrt[\square]{18(18-7)(18-14)(18-15)} \\ A=\sqrt[\square]{18*11*4*3} \\ A=\sqrt[\square]{2376} \\ A=48.7\text{ } \end{gathered}`

Area = 48.7 square units.

ii. a = 11 , b = 12 , c = 16

`\begin{gathered} s=(11+12+16)/(2) \\ s=19.5 \\ \text{thus} \\ A=\sqrt[]{19.5(19.5-11)(19.5-12)(19.5-16)} \\ A=\sqrt[]{19.5*8.5*7.5*3.5} \\ A=65.96\approx66 \end{gathered}`

Area = 66 square units