Area & Perimeter

G 10
Redraw the shapes, one imposed on the other.
T: A large part of the square is covered by the other rectangle.
But part of the square is not covered, and part of the other
rectangle does not cover any of the square. Let’s call the
three parts A, B, and C.
Now the square has two parts, A and C, and the rectangle
has two parts, A and B. Which do you think has larger area,
B or C?
Trace two adjacent sides of the square, and then two adjacent sides
of the other rectangle as you note that the total lengths are the same
(50 cm, or half of the perimeter) in both cases.
Conclude that the short dimension of C is the same as the short
dimension of B.
T: We are concerned with which rectangle has more area,
B or C. How can we find the area of any rectangle?
S: Multiply its length times its width.
T: Rectangles B and C have the same width.
But do they have the same length?
Trace the length of rectangle C and then the length of rectangle B.
S: No, rectangle B is not as long as rectangle C.
Observe that the length of B is shorter than the side of the square,
but the length of C is the side of the square.
T: So do the rectangles B and C have the same area?
S: No, C has larger area.
T: So which pen would have more area, A with B or A with C?
S: A with C.
T: So the square pen is the best solution for the farmer.
G-54
IG-III