See following link:

April 12, 2018 - 6:00am

#1
Area of Right Triangle Using Radius of Incircle

engineering stress and strain definition formula for composite figures algebraic substitution calculator surface area integral calculator submerged unit weight of soil wsd method inscribed circle in square double integral problems circles angles and arcs truss crane differentiation of trig centroid incenter circumcenter and orthocenter cyclic quadrilateral formula ladder problem physics the sum of arithmetic sequence formula for a triangle perimeter deceleration equation sine cosine laws triangular load shear and moment diagram explain a proof of the pythagorean theorem superposition solved problems calculating shear stress in a beam 4pir integrating factors differential equations method of sections statics an inscribed angle formulas of triangle angle of elevation trigonometry torsional shear stress calculator homogeneous ordinary differential equation coefficient of binomial expansion shear strength of carbon steel types of beams in mechanics curved beam bending stress goat math problem indefinite intergrals triangles perimeter pratt trusses how to calculate overturning moment lateral surface area of a right circular cone ductile iron modulus of elasticity geometric sequence formulas trig function derivatives summation geometric series torsional stress formula vertex of a triangle cantilever loading standard parabola prove the law of cosines altitude of a cylinder strength materials ydx xdy how to calculate the radius of gyration internally tangent circles formula for curved surface area of a cone fx math solver definition of elipse spherical right triangle formula of tan2x moment of inertia examples lateral area of the cylinder ferdinand beer mechanics of materials solutions average shear stress in a pin compressive stress formula stress strain curve for low carbon steel calculating resultant force forces and pulleys central angle definition math parabolic curves volume triangular pyramid laplace transforms examples torsional stress equation

Good day sir. I made the attempt to trace the formula in your link, $A = R(a + b - c)$, but with no success. I notice however that at the bottom there is this line, $R = (a + b - c)/2$.

The radius of inscribed circle however is given by $R = (a + b + c)/2$ and this is true for any triangle, may it right or not. I have this derivation of radius of incircle here: http://vkd-studio.ru/node/581.

I think that is the reason why that formula for area don't add up.

Thank you for reviewing my post. I think, if you'll look again, you'll find my formula for the area of a right triangle is A = R (a + b - R), not A = R (a+ b - c).

Also, by your formula, R = (a + b + c) / 2 would mean that R for a 3, 4, 5 triangle would be 6.00, whereas, mine R = (a + b - c) /2 gives a R of 1.00.

See link below for another example:

My bad sir, I was not so keen in reading your post, even my own formula for

Ris actually wrong here. It should be $R = A_t / s$, not $R = (a + b + c)/2$ because $(a + b + c)/2 = s$ in the link I provided.Anyway, thank again for the link to Dr. Math page. I never look at the triangle like that, the reason I was not able to arrive to your formula. Though simpler, it is more clever. I will add to this post the derivation of your formula based on the figure of Dr. Math. Thanks.

No problem. Thanks for adding the new derivation. Nice presentation.

For the convenience of future learners, here are the formulas from the given link:

$A = r(a + b - r)$

$r = \dfrac{a + b - c}{2}$

Derivation:From the figure below,

ADis congruent toAEandBFis congruent toBE. Hence:Area

ADO= AreaAEO=A_{2}Area

BFO= AreaBEO=A_{3}Area of triangle

ABC$A = A_1 + 2A_2 + 2A_3$

$A = r^2 + 2\left[ \dfrac{r(b - r)}{2} \right] + 2\left[ \dfrac{r(a - r)}{2} \right]$

$A = r^2 + (br - r^2) + (ar - r^2)$

$A = br + ar - r^2$

$A = r(a + b - r)$ ← the formula

Radius of inscribed circle:

$AE + EB = AB$

$(b - r) + (a - r) = c$

$a + b - c = 2r$

$r = \dfrac{a + b - c}{2}$ ← the formula