Question

If D, E , & F and the mid point of the side BC , CA , and AB respectively of a triangle ABC . If AB= 6.2 cm, BC = 5.6 cm and CA =4.6 cm . find the perimeter of :
1) Trapezium FBCE and
2) triangle DEF

Answer 1

Answer:

1) 13.8 cm

2) 8.2 cm

Step-by-step explanation:

The key is to notice that by joining the midpoints D, E, F to each other, triangle ABC is cut up into 4 congruent triangles.

So...

1) Perimeter of FBCE

= FB + BC + CE + EF

= AB/2 + BC + CA/2 + BC/2

= 3.1 cm + 5.6 cm + 2.3 cm + 2.8 cm

= 13.8 cm

2) Perimeter of DEF

= DE + EF + FD

= AB/2 + BC/2 + CA/2

= 3.1 cm + 2.8 cm + 2.3 cm

= 8.2 cm