Find the area of the triangle with the coorinates a) (acostheta_1,bsintheta_1 , (acostheta_2,bsintheta_2 (acostheta_3,bsintheta_3 B) (am_1^2, 2am_1) , (am_2^2, 2am_2), (am_3^2, 2am_3)?

There are two separate sets of coordinates.

1 Answer
Dec 21, 2017

See below.

Explanation:

Given a triangle with vertices at

p_1 = (x_1,y_1)
p_2=(x_2,y_2)
p_3 = (x_3,y_3)

Area can be computed as

A = 1/2 abs(det((x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1)))

so in the first case

A = 1/2 abs(det((a m_1^2, a m_1, 1),(a m_2^2, a m_2, 1),(a m_3^2, a m_3, 1))) = a^2/2 abs((m_1-m_2)(m_1-m_3)(m_2-m_3))

analogously

A = (ab)/2abs(Sin(theta_1 - theta_2) + Sin(theta_3 - theta_1) + Sin(theta_2 - theta_3))