The sides of a triangle are 8, 10, and 8.9? Find the area of the triangle. Round to 2 decimal places

1 Answer
Apr 11, 2018

#"area "~~33.92" to 2 dec. places"#

Explanation:

#"given the 3 sides of the triangle we can calculate the "#
#"area (A) using "color(blue)"Heron's formula"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(A=sqrt(s(s-a)(s-b)(s-c))color(white)(2/2)|)))#

#"where s is the semi-perimeter and a, b , c are the 3 sides"#

#color(blue)"calculate semi-perimeter (s)"#

#"let "a=8, b=10" and "c=8.9#

#s=(a+b+c)/2=(8+10+8.9)/2=13.45#

#color(blue)"calculate area (A)"#

#A=sqrt(13.45(13.45-8)(13.45-10)(13.45-8.9))#

#color(white)(A)=sqrt(13.45xx5.45xx3.45xx4.55)#

#color(white)(A)~~33.92" to 2 dec. places"#