A kite with a 10cm height and a 5 cm width.

Question

1. By what factor does the area change if both diagonals are doubled? Explain.

2. By what factor does the area change if one diagonal is doubled? Explain.

Answer 1

1) Area of the kite = (p*q)/2

Where p and q are both the diagonals.

A(initial) = (p*q)/2
A(final) = ((2p)*(2q))/2
= 4(p*q)/2
= 4*A(inital)

It increases by a factor of 4.

2)

A(initial) = (p*q)/2
A(final) = ((2p)*(q))/2
= 2(p*q)/2
= 2*A(inital)

It increases by a factor of 2.