Question

In the adjoining figure; D, E and F are the mid-points of BC, CA and AB, respectively. If AB = 6 cm, BC = 8 cm and AC = 5.6 cm, find :

1. perimeter of ΔDEF
2. perimeter of ◻ABDE

Answer 1

Given:

ΔABC with D, E, F mid‑points of BC, CA, AB respectively.

AB = 6 cm, BC = 8 cm, AC = 5.6 cm.

Step-wise calculation:

1. Use the Midpoint Theorem:

Each segment joining mid‑points is parallel to the third side and equals half its length. 

Hence, `DE = 1/2 xx AB`

`EF = 1/2 xx BC`

`FD = 1/2 xx AC`

2. Compute those lengths:

`DE = 1/2 xx 6`

= 3.0 cm

`EF = 1/2 xx 8`

= 4.0 cm

`FD = 1/2 xx 5.6`

= 2.8 cm

3. Perimeter of ΔDEF

= DE + EF + FD

= 3.0 + 4.0 + 2.8

= 9.8 cm

4. For quadrilateral ABDE taken in order A → B → D → E → A, its side lengths are:

AB = 6.0 cm

BD = `1/2` × BC

= 4.0 cm

DE = 3.0 cm   ...(From above)

EA = `1/2` × AC

= 2.8 cm

5. Perimeter of ◻ABDE

= AB + BD + DE + EA

= 6.0 + 4.0 + 3.0 + 2.8

= 15.8 cm