In △abc, point p∈ ab is so that ap: bp=1: 3 and point m is the midpoint of segment cp . find the area of △abc if the area of △bmp is equal to 21m2.

Area of  ΔABC = 56m².

Explanation:

Since we have given that

point P∈ AB, such that AP:BP=1:3

Point M is the midpoint of segment CP.

Now, we have given that

Area of ΔBMP=21 m²

Since M is the mid-point of CP, so,

Area of ΔCMP= 21 m².

So, Area of ΔBCP = 21+21=42 m²

According to question,

So, area of ΔABC is given by

Hence, area of  ΔABC =56m².

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step-by-step explanation: