If m is any point in the interior of apor ma, mb and mc be the perpendicular on sides pq and pr respectively, then
Answers
If m is any point in the interior of triangle pqr, ma,mb, mc are the perpendicular to side pq,qr,pr respectively then the Area of ∆PQR = ½ * [PQ*AM + QR*BM + PR*CM].
Step-by-step explanation:
Required formula:
Area of a triangle = [½ * base * height] sq. units
It is given that,
M is an interior point of the triangle PQR and lines drawn intersects each side PQ, QR & PR at A, B & C respectively, as shown in the figure attached below, such that
AM ⊥ PQ
BM ⊥ QR
CM ⊥ PR
Now, we have
Area of ∆PQR = [Area of ∆PQM] + [Area of ∆QRM ] + [Area of triangle ∆PRM] ….. (i)
Thus,
Referring to the figure and based on the formula, we can write eq. (i) as,
Area of ΔPQR
= [1/2 * PQ * AM] + [1/2 * QR * BM] + [1/2 * PR * CM]
= ½ * [PQ*AM + QR*BM + PR*CM]
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Answer:
Step-by-step explanation: