MHB Calculate the area of a triangle knowing its 3 heights

[loquetedigo]

Calculate the area of a triangle knowing its 3 heights

ha = 3 m
hb = 4 m
hc = 5 m

NOTE = You can use the online triangle calculator TrianCal to see and draw the results.
NOTE = Do not use the values ??of responses.

A) 10.03 m2
B) 10.04 m2
C) 10.05 m2
D) Imposible

 

[Greg]

Can you apply Heron's formula?

 

[loquetedigo]

Can you apply Heron's formula?

thanks...
Next, denoting the altitudes from sides a, b, and c respectively as ha, hb, and hc, and denoting the semi-sum of the reciprocals of the altitudes as H = (h_a^{-1} + h_b^{-1} + h_c^{-1})/2 we have[11]

A^{-1} = 4 \sqrt{H(H-h_a^{-1})(H-h_b^{-1})(H-h_c^{-1})}.