Question

Please fill in the boxes with correct answers (see attachment for question)

Answer 1

Explanation:

Point R is the mid point of side FE Using mid point formula coodinates of F are (3a,b)

In triangle DEF, DF = base = 4a and height = 2b.

Hence area of triangle DEF = 1/2 hy = 4ab

In triangle QRP, base QR = line joining mid points of sides DE and EF

= 1/2 (DF) = 2a

Height =b

So area of triangle DEF = 1/2 (2a)b = ab

i.e. Area of triangle DEF = 4 times triangle QRD

It follows that in an isosceles triangle, if QR is the mid points of isosceles sides, then triangle QRD has 1/4 times area of triangle DEF