Question

In this given figure,M is the mid point od AB and AD perpendicular to BD. If BC=6 cm amr AD=8 cm, find the area of triangle AMC

Answer 1

Given:

In this given figure, M is the mid-point of AB and AD perpendicular to BD. If BC = 6 cm and AD = 8 cm

To find:

The area of triangle AMC

Solution:

M is the mid-point of AB and is drawn from the vertex C

∴ CM is the median of Δ ABC . . . [since a median of a triangle joins the  vertex and the midpoint of the opposite side]

In Δ ABC, we have

BC = base = 6 cm

AD = perpendicular height on the extended base BD = 8 cm

∴ Area of Δ ABC is,

= $\frac{1}{2} \times base \times height$

= $\frac{1}{2} \times BC \times AD$

= $\frac{1}{2} \times 6 \times 8$

= $\bold{24\:cm^2}$

We know that → a median of a triangle divides the triangle into two smaller triangles of equal area.

Therefore, we get

The area of Δ AMC is,

= $\frac{1}{2} \times [Area \:of\:\triangle \:ABC ]$

= $\frac{1}{2} \times 24$

= $\bold{12\:cm^2}$

Thus, the area of triangle AMC is → 12 cm².

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