Author: Anthony C.M. Or. Education Bureau, Hong Kong.

Mark New Area

See the difference

See the Difference

Drag the red point to decrease the length by 1 cm 
and increase the width by 1 cm.

Is the perimeter changed? 
Is the area larger or smaller?  Click 'See the difference'.

Length

Width

Perimeter

Area

Back

When is the area largest?  Click 'Mark New Area' and try again.

perimeter = 20 (slider from 4 to 64, step 4)
a: x + y = perimeter / 2
P = Point(Segment[Intersect[a, x = 1], Intersect[a, y = 1]])
O = (0, 0)
A: (x(P), 0)
B: (0, y(P))
b = PolyLine(O, A, P, B, O)
Q = (9, 1)
Q_1: (x(Q), 0)
Q_2: (0, y(Q))
t = 0 (slider from 0 to 1, step 0.05)
C = Intersect(Segment[A, P], Segment[Q, Q_2])
poly1, o, a_1, c, q_2 = Polygon(O, A, C, Q_2)
e = Segment(Q_2, C)
f = Segment(C, Q)
k = LineBisector(Q_2, C)
l = LineBisector(B, Q)
I = Intersect(k, l)
A'_1 = Rotate(A, 90° * t, I)
J = Rotate(Q_1, 90° * t, I)
Q'_1 = Rotate(Q, 90° * t, I)
C'_1 = Rotate(C, 90° * t, I)
poly3, a'_1, j_1, q'_1, c'_1 = Polygon(A'_1, J, Q'_1, C'_1)
D = Intersect(Segment[B, P], Segment[Q, Q_1])
poly2, o_1, q_1, d, b_1 = Polygon(O, Q_1, D, B)
g = LineBisector(D, Q_1)
h = LineBisector(Q, A)
E = Intersect(h, g)
B' = Rotate(B, (-90)° * t, E)
D' = Rotate(D, (-90)° * t, E)
Q' = Rotate(Q, (-90)° * t, E)
F = Rotate(Q_2, (-90)° * t, E)
poly4, b', d', q', f_1 = Polygon(B', D', Q', F)
A2 = 9
B2 = 1
C2 = 20
D2 = 9
show_m = false
i: t ≟ 0
j: t ≟ 0
m: t ≟ 0