📐How to Find The Area of the Triangle ? | 2 Methods

In this lesson, we learned two methods to find the area of a triangle. We used the sine area formula and also applied the concept of similar triangles. Additionally, we made use of information about quadratic equations.

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#geometry #math #triangles

[joseluishablutzelaceijas]

Another solution would be: Draw a perpendicular through C to the extension of AD, say the perpendicular and the extension intersect at P. The length of segment PC is then, due to those 30°, equal to sqrt(3)/2, and the height of triangle BDA relative to AD is, due to the BD:DC = 2:1 ratio, equal to sqrt(3). Thus, the angle BAD is equal to 60° and the area is then equal to 2*sqrt(3)/2 = sqrt(3).

[howardaltman]

Another approach is to locate point E on AC such that DE//BA. This makes ΔBAC~ΔDEC by AA~ with a scale factor of 3:1; hence, DE=2/3 and AE=2/3√3. DE and AE along with the given 30° force ∠ADE=60°. Hence, ∠BAD=60°, ∠BAC=90°, and the area is √3. Neat question!

[yassinehinnach]

In method 1, by noticing that tan 30 = 1/sqrt(3) we can tell that we have a right angle which eliminates the need for some of the calculations in the video.