Steve has a square patio with sides of length 9 feet. He plans to enlarge it to a rectangular patio by increasing the length by 3 feet and the width by 2 feet. How many square feet in area will be added to the

patio?

06

O 12

0 29

O 51

51ft^2

Step-by-step explanation:

Given data

Side of square patio= 9ft

Area= 9*9= 81 ft^2

New length = 9+3= 12ft

New Widht = 9+2= 11ft

New Area= 12*11

New Area= 132ft^2

Hence the area added is

=132-81

=51ft^2

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

i get you, what you should do is think of the positive things that would come out of it. it will make yours parents proud and raise your grade. you should always try and if you can't focus tell the teacher.