Question

HELP NEEDED. 37 POINTSI just need the answers

Answer 1

Answer:

Part 1) $P=[2\sqrt{29}+\sqrt{18}]\ units$ or $P=15.01\ units$

Part 2) $P=2[\sqrt{20}+\sqrt{45}]\ units$ or $P=22.36\ units$

Part 3) $P=4[\sqrt{13}]\ units$ or $P=14.42\ units$

Part 4) $P=[19+\sqrt{17}]\ units$ or $P=23.12\ units$

Part 5) $P=2[\sqrt{17}+\sqrt{68}]\ units$ or $P=24.74\ units$

Part 6) $A=36\ units^{2}$

Part 7) $A=20\ units^{2}$

Part 8) $A=16\ units^{2}$

Part 9) $A=10.5\ units^{2}$

Part 10) $A=6.05\ units^{2}$

Step-by-step explanation:

we know that

The formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

Part 1) we have the triangle ABC

$A(0,3),B(5,1),C(2,-2)$

step 1

Find the distance AB

$A(0,3),B(5,1)$

substitute in the formula

$AB=\sqrt{(1-3)^{2}+(5-0)^{2}}$

$AB=\sqrt{(-2)^{2}+(5)^{2}}$

$AB=\sqrt{29}\ units$

step 2

Find the distance BC

$B(5,1),C(2,-2)$

substitute in the formula

$BC=\sqrt{(-2-1)^{2}+(2-5)^{2}}$

$BC=\sqrt{(-3)^{2}+(-3)^{2}}$

$BC=\sqrt{18}\ units$

step 3

Find the distance AC

$A(0,3),C(2,-2)$

substitute in the formula

$AC=\sqrt{(-2-3)^{2}+(2-0)^{2}}$

$AC=\sqrt{(-5)^{2}+(2)^{2}}$

$AC=\sqrt{29}\ units$

step 4

Find the perimeter

The perimeter is equal to

$P=AB+BC+AC$

substitute

$P=[\sqrt{29}+\sqrt{18}+\sqrt{29}]\ units$

$P=[2\sqrt{29}+\sqrt{18}]\ units$

or

$P=15.01\ units$

Part 2) we have the rectangle ABCD

$A(-4,-4),B(-2,0),C(4,-3),D(2,-7)$

Remember that in a rectangle opposite sides are congruent

step 1

Find the distance AB

$A(-4,-4),B(-2,0)$

substitute in the formula

$AB=\sqrt{(0+4)^{2}+(-2+4)^{2}}$

$AB=\sqrt{(4)^{2}+(2)^{2}}$

$AB=\sqrt{20}\ units$

step 2

Find the distance BC

$B(-2,0),C(4,-3)$

substitute in the formula

$BC=\sqrt{(-3-0)^{2}+(4+2)^{2}}$

$BC=\sqrt{(-3)^{2}+(6)^{2}}$

$BC=\sqrt{45}\ units$

step 3

Find the perimeter

The perimeter is equal to

$P=2[AB+BC]$

substitute

$P=2[\sqrt{20}+\sqrt{45}]\ units$

or

$P=22.36\ units$

Part 3) we have the rhombus ABCD

$A(-3,3),B(0,5),C(3,3),D(0,1)$

Remember that  in a rhombus all sides are congruent

step 1

Find the distance AB

$A(-3,3),B(0,5)$

substitute in the formula

$AB=\sqrt{(5-3)^{2}+(0+3)^{2}}$

$AB=\sqrt{(2)^{2}+(3)^{2}}$

$AB=\sqrt{13}\ units$

step 2

Find the perimeter

The perimeter is equal to

$P=4[AB]$

substitute

$P=4[\sqrt{13}]\ units$

or

$P=14.42\ units$

Part 4) we have the quadrilateral ABCD

$A(-2,-3),B(1,1),C(7,1),D(6,-3)$

step 1

Find the distance AB

$A(-2,-3),B(1,1)$

substitute in the formula

$AB=\sqrt{(1+3)^{2}+(1+2)^{2}}$

$AB=\sqrt{(4)^{2}+(3)^{2}}$

$AB=5\ units$

step 2

Find the distance BC

$B(1,1),C(7,1)$

substitute in the formula

$BC=\sqrt{(1-1)^{2}+(7-1)^{2}}$

$BC=\sqrt{(0)^{2}+(6)^{2}}$

$BC=6\ units$

step 3

Find the distance CD

$C(7,1),D(6,-3)$

substitute in the formula

$CD=\sqrt{(-3-1)^{2}+(6-7)^{2}}$

$CD=\sqrt{(-4)^{2}+(-1)^{2}}$

$CD=\sqrt{17}\ units$

step 4

Find the distance AD

$A(-2,-3),D(6,-3)$

substitute in the formula

$AD=\sqrt{(-3+3)^{2}+(6+2)^{2}}$

$AD=\sqrt{(0)^{2}+(8)^{2}}$

$AD=8\ units$

step 5

Find the perimeter

The perimeter is equal to

$P=AB+BC+CD+AD$

substitute

$P=[5+6+\sqrt{17}+8]\ units$

$P=[19+\sqrt{17}]\ units$

or

$P=23.12\ units$

Part 5) we have the quadrilateral ABCD

$A(-1,5),B(3,6),C(5,-2),D(1,-3)$

step 1

Find the distance AB

$A(-1,5),B(3,6)$

substitute in the formula

$AB=\sqrt{(6-5)^{2}+(3+1)^{2}}$

$AB=\sqrt{(1)^{2}+(4)^{2}}$

$AB=\sqrt{17}\ units$

step 2

Find the distance BC

$B(3,6),C(5,-2)$

substitute in the formula

$BC=\sqrt{(-2-6)^{2}+(5-3)^{2}}$

$BC=\sqrt{(-8)^{2}+(2)^{2}}$

$BC=\sqrt{68}\ units$

step 3

Find the distance CD

$C(5,-2),D(1,-3)$

substitute in the formula

$CD=\sqrt{(-3+2)^{2}+(1-5)^{2}}$

$CD=\sqrt{(-1)^{2}+(-4)^{2}}$

$CD=\sqrt{17}\ units$

step 4

Find the distance AD

$A(-1,5),D(1,-3)$

substitute in the formula

$AD=\sqrt{(-3-5)^{2}+(1+1)^{2}}$

$AD=\sqrt{(-8)^{2}+(2)^{2}}$

$AD=\sqrt{68}\ units$

step 5

Find the perimeter

The perimeter is equal to

$P=\sqrt{17}+\sqrt{68}+\sqrt{17}+\sqrt{68}$

substitute

$P=2[\sqrt{17}+\sqrt{68}]\ units$

or

$P=24.74\ units$

The complete answer in the attached file

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