Question

if the length of median of triangle ABC are 6 8 10 then area of triangle is equal to

Answer 1

sides 6,8,10 indicates that the triangle is right angled , with 10 as the hypotenuse.


then the area of triangle

1/ 2 x base x height

= 1/2 x 6 x 8

= 24 cm^2

Answer 2

The area of triangle ABC is 32sq.units

Step-by-step explanation:

Given:

In ΔABC

length of medians as 6, 8, 10

To find:

area of ΔABC

Solution:

Let, m1= 6, m2=8, m3=10

Now, we find the semi perimeter (s) using the lengths of median

∴ s= m1+m2+m3

             2

∴ s= 6+8+10

           2

∴ s = 24

         2

∴ s = 12

Now, we find the area of the triangle using the median values

Area of triangle = 4 √s(s-m1) (s-m2) (s-m3)

                             3

∴ Area of ΔABC=  $\frac{4}{3} \sqrt{12(12-6) (12-8) (12-10)$

∴ Area of ΔABC= $\frac{4}{3} \sqrt{12 (6) (4) (2)$

∴ Area of ΔABC= $\frac{4}{3} \sqrt{12 (48)$

∴ Area of ΔABC= $\frac{4}{3} \sqrt{576$

∴ Area of ΔABC= $\frac{4}{3} (24)$

∴ Area of ΔABC= $\frac{96}{3}$

∴ Area of ΔABC= $32$

∴ Area of ΔABC= 32 sq. units

Thus, the area of the triangle is equal to 32 sq. units

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