Answer:
690 sq in
Step-by-step explanation:
SA = LA + 2B where LA is the lateral area and B is the area of the base
The triangular base has an area of
B = 1/2bh 1/2(5)(12) = 30
LA = ph where p is the perimeter of the base and h is the height of the prism
LA = (12 + 5 + 13)(21) = 30(21) = 630
SA = 630 + 2(30) = 630 + 60 = 690 sq in
Step-by-step explanation:
(5.2+3.1)+7.4=5.2+(3.1+7.4)
(8.3)+7.4=5.2+(10.5)
15.7=15.7
hence,L.H.S =R.H.S PROVED
Let the sides of the polygon (which is a triangle, by the way) be x, y and z. The sum of x, y and z is the perimeter of the original poly, and this equals 18 cm.
Letting f be the scale factor, f(18 cm) = 12 cm. Then f=2/3.
The dilation reduces the size of the polygon by a factor of 1/3, producing a similar polygon which is 2/3 the size of the original one.
In each case we have 3 side lengths but no angles. We can use Heron's formula to obtain the area in each case. Look up Heron's formula. In one version of this formula, p is half the actual perimeter, meaning that p is 18 cm / 2 for the first triangle and 12 cm / 2 for the second.
The area of the first triangle would be
A18 = sqrt( 9(9-x)(9-y)(9-z) )
whereas
A12 = sqrt( 6(6-x*a)(6-y*a)(6-z*a) ), where a represents the dilation factor 2/3.
Then the ratio of the areas of the 2 triangles is
sqrt( 6(6-x*a)(6-y*a)(6-z*a) )
---------------------------------------
sqrt( 9(9-x)(9-y)(9-z) )
50 - [(6² - 24) + 9√25]
= 50 - [36 - 24 + 9*5]
= 50 - [12 + 45]
= 50 - 57
= -7
Answer:
Option D $26,792
Step-by-step explanation:
When producing 427 printers, the cost of production is 427*$48.28=$20,615.56
When selling each printer, profit per printer is $163.95 - $48.28= $115.67
Total money after selling the 427 printers is 427*$163.95 =$70006.65
Subtracting cost of production from value of sales we deduce
$70006.65-$20,615.56=$49391.09
Non-profit overhead expenses will be the difference between the expected profit and the actual profit earned
$49391.09
-$22,599.09.=$26,792
Therefore, option D, $26,792 is the right choice
