The given figure shows Î”ABC Points D, E and F are the mid-points of sides AB, AC and BC - Maths - Areas of Parallelograms and Triangles

Question

The given figure shows Î”ABC Points D, E and F are
the mid-points of sides AB, AC and BC respectively Sides AB, BC and
CA measure 6 cm, 10 cm and 8 cm respectively

What is the area of tri DEF

Gursheen kaur. · Accepted Answer

As we know that if lines are drawn through D, E, F respectively to the sides DE, FD and EF which forms ΔDEF.

$\Rightarrow D E = \frac{1}{2} B C, E F = \frac{1}{2} A B, F D = \frac{1}{2} C A \Rightarrow D E = \frac{1}{2} \times 10, E F = \frac{1}{2} \times 6, F D = \frac{1}{2} \times 8 \Rightarrow D E = 5 c m = a, E F = 3 c m = b, F D = 4 c m = c$

Now, perimeter of ΔDEF , s = (5+3+4)/2= 12/2=6 cm.

∴ Area of ΔDEF = $\sqrt{s (s - a) (s - b) (s - c)}$

$= \sqrt{6 (6 - 5) (6 - 3) (6 - 4)} = \sqrt{6 \times 1 \times 3 \times 2} = \sqrt{36} = 6 s q c m .$

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The given figure shows ΔABC. Points D, E and F are the mid-points of sides AB, AC and BC respectively. Sides AB, BC and CA measure 6 cm, 10 cm and 8 cm respectively. What is the area of tri DEF

The given figure shows ΔABC. Points D, E and F are the mid-points of sides AB, AC and BC respectively. Sides AB, BC and CA measure 6 cm, 10 cm and 8 cm respectively.

What is the area of tri DEF