we know that
The area of a rectangle is equal to
\(A=L*W\)
where
L is the length side of the rectangle
w is the width side of the rectangle
To determine the solution we will proceed to graph and calculate the area of each rectangle
case 1) \(A(-9, 8), B(-5, 5), C(1, 13), D(-3, 16)\)
using a graph tool
see the attached figure N \(1\)
Find the distance BC (Length side)
\(d=\sqrt{(y2-y1)^{2} +(x2-x1)^{2}}\)
\(d=\sqrt{(13-5)^{2} +(1+5)^{2}}\)
\(d=\sqrt{(8)^{2} +(6)^{2}}\)
\(d=10\ units\)
Find the distance AB (Width side)
\(d=\sqrt{(y2-y1)^{2} +(x2-x1)^{2}}\)
\(d=\sqrt{(5-8)^{2} +(-5+9)^{2}}\)
\(d=\sqrt{(-3)^{2} +(4)^{2}}\)
\(d=5\ units\)
Find the area of rectangle ABCD
\(A=L*W\)
\(A=10*5\)
\(A=50\ units^{2}\)
The area of the rectangle ABCD is \(50\ units^{2}\)
case 2) \(E(30, 20), F(39, 29), G(49, 19), H(40, 10)\)
using a graph tool
see the attached figure N \(2\)
Find the distance EH (Length side)
\(d=\sqrt{(y2-y1)^{2} +(x2-x1)^{2}}\)
\(d=\sqrt{(10-20)^{2} +(40-30)^{2}}\)
\(d=\sqrt{(-10)^{2} +(10)^{2}}\)
\(d= \sqrt{200}\ units\)
Find the distance EF (Width side)
\(d=\sqrt{(y2-y1)^{2} +(x2-x1)^{2}}\)
\(d=\sqrt{(29-20)^{2} +(39-30)^{2}}\)
\(d=\sqrt{(9)^{2} +(9)^{2}}\)
\(d= \sqrt{162}\ units\)
Find the area of rectangle EFGH
\(A=L*W\)
\(A=\sqrt{200} *\sqrt{162}\)
\(A=180\ units^{2}\)
The area of the rectangle EFGH is \(180\ units^{2}\)
case 3) \(I(-6, 2), J(2, 2), K(2, -8), L(-6, -8)\)
using a graph tool
see the attached figure N \(3\)
Find the distance JK (Length side)
\(d=\sqrt{(y2-y1)^{2} +(x2-x1)^{2}}\)
\(d=\sqrt{(-8-2)^{2} +(2-2)^{2}}\)
\(d=\sqrt{(-10)^{2} +(0)^{2}}\)
\(d=10\ units\)
Find the distance KL (Width side)
\(d=\sqrt{(y2-y1)^{2} +(x2-x1)^{2}}\)
\(d=\sqrt{(-8+8)^{2} +(-6-2)^{2}}\)
\(d=\sqrt{(0)^{2} +(-8)^{2}}\)
\(d=8\ units\)
Find the area of rectangle IJKL
\(A=L*W\)
\(A=10*8\)
\(A=80\ units^{2}\)
The area of the rectangle IJKL is \(80\ units^{2}\)
case 4) \(M(5, 5), N(11, 5), O(11, -5), P(5, -5)\)
using a graph tool
see the attached figure N \(4\)
Find the distance NO (Length side)
\(d=\sqrt{(y2-y1)^{2} +(x2-x1)^{2}}\)
\(d=\sqrt{(-5-5)^{2} +(11-11)^{2}}\)
\(d=\sqrt{(-10)^{2} +(0)^{2}}\)
\(d=10\ units\)
Find the distance OP (Width side)
\(d=\sqrt{(y2-y1)^{2} +(x2-x1)^{2}}\)
\(d=\sqrt{(-5+5)^{2} +(5-11)^{2}}\)
\(d=\sqrt{(0)^{2} +(-6)^{2}}\)
\(d=6\ units\)
Find the area of rectangle MNOP
\(A=L*W\)
\(A=10*6\)
\(A=60\ units^{2}\)
The area of the rectangle MNOP is \(60\ units^{2}\)
case 5) \(Q(10, 0), R(15, 5), S(25, -5), T(20, -10)\)
using a graph tool
see the attached figure N \(5\)
Find the distance RS (Length side)
\(d=\sqrt{(y2-y1)^{2} +(x2-x1)^{2}}\)
\(d=\sqrt{(-5-5)^{2} +(25-15)^{2}}\)
\(d=\sqrt{(-10)^{2} +(10)^{2}}\)
\(d= \sqrt{200}\ units\)
Find the distance ST (Width side)
\(d=\sqrt{(y2-y1)^{2} +(x2-x1)^{2}}\)
\(d=\sqrt{(-10+5)^{2} +(20-25)^{2}}\)
\(d=\sqrt{(-5)^{2} +(-5)^{2}}\)
\(d= \sqrt{50}\ units\)
Find the area of rectangle QRST
\(A=L*W\)
\(A=\sqrt{200} *\sqrt{50}\)
\(A=100\ units^{2}\)
The area of the rectangle QRST is \(100\ units^{2}\)
case 6) \(U(0, 5), V(15, 20), W(25, 10), X(10, -5)\)
using a graph tool
see the attached figure N \(6\)
Find the distance WX (Length side)
\(d=\sqrt{(y2-y1)^{2} +(x2-x1)^{2}}\)
\(d=\sqrt{(-5-10)^{2} +(10-25)^{2}}\)
\(d=\sqrt{(-15)^{2} +(-15)^{2}}\)
\(d= \sqrt{450}\ units\)
Find the distance VW (Width side)
\(d=\sqrt{(y2-y1)^{2} +(x2-x1)^{2}}\)
\(d=\sqrt{(10-20)^{2} +(25-15)^{2}}\)
\(d=\sqrt{(-10)^{2} +(10)^{2}}\)
\(d= \sqrt{200}\ units\)
Find the area of rectangle UVWX
\(A=L*W\)
\(A=\sqrt{200} *\sqrt{450}\)
\(A=300\ units^{2}\)
The area of the rectangle UVWX is \(300\ units^{2}\)
