Suppose the side length of a square is \color{S_COLOR}{S}
. What is its area?
The area of a square is K = s \cdot s = s^2
.
Substituting in s = \color{S_COLOR}{S}
gives K = \color{S_COLOR}{S}^2 = \color{K_COLOR}{S * S}
.
Suppose the side length of a square is \color{S_COLOR}{S}
. What is its perimeter?
The perimeter of a square is P = s + s + s + s = 4s
.
Substituting in s = \color{S_COLOR}{S}
gives P = 4\cdot\color{S_COLOR}{S} = \color{P_COLOR}{4 * S}
.
Suppose the area of a square is \color{K_COLOR}{S * S}
. What is its side length?
The area of a square is K = s \cdot s = s^2
, so s = \sqrt{K}
.
Substituting in K = \color{K_COLOR}{S * S}
gives s = \sqrt{\color{K_COLOR}{S * S}} = \color{S_COLOR}{S}
.
Suppose the area of a square is \color{K_COLOR}{S * S}
. What is its perimeter?
The area of a square is K = s \cdot s = s^2
, so s = \sqrt{K}
.
Substituting in K = \color{K_COLOR}{S * S}
gives s = \sqrt{\color{K_COLOR}{S * S}} = \color{S_COLOR}{S}
.
Now find the perimeter using P = s + s + s + s = 4s
.
Substituting in s = \color{S_COLOR}{S}
gives P = 4\cdot\color{S_COLOR}{S} = \color{P_COLOR}{4 * S}
.
Suppose the perimeter of a square is \color{P_COLOR}{4 * S}
. What is its side length?
The perimeter of a square is P = s + s + s + s = 4s
, so s = P/4
.
Substituting in P = \color{P_COLOR}{4 * S}
gives s = \color{P_COLOR}{4 * S}/4 = \color{S_COLOR}{S}
.
Suppose the perimeter of a square is \color{P_COLOR}{4 * S}
. What is its area?
The perimeter of a square is P = s + s + s + s = 4s
, so s = P/4
.
Substituting in P = \color{P_COLOR}{4 * S}
gives s = \color{P_COLOR}{4 * S}/4 = \color{S_COLOR}{S}
.
Now find the area using K = s \cdot s = s^2
.
Substituting in s = \color{S_COLOR}{S}
gives K = \color{S_COLOR}{S}^2 = \color{K_COLOR}{S * S}
.
Suppose a rectangle has length \color{L_COLOR}{L}
and width \color{W_COLOR}{W}
. What is its area?
The area of a rectangle is K = lw
.
Substituting in l = \color{L_COLOR}{L}
and w = \color{W_COLOR}{W}
gives K = \color{L_COLOR}{L} \cdot \color{W_COLOR}{W} = \color{K_COLOR}{L * W}
.
Suppose a rectangle has length \color{L_COLOR}{L}
and width \color{W_COLOR}{W}
. What is its perimeter?
The area of a rectangle is P = l + w + l + w = 2(l + w)
.
Substituting in l = \color{L_COLOR}{L}
and w = \color{W_COLOR}{W}
gives P = 2 (\color{L_COLOR}{L} + \color{W_COLOR}{W}) = \color{P_COLOR}{2 * L + 2 * W}
.