Hi,



parallelogram has an area of 720 sq.cm. and a perimeter of 152 cm. 

one of the interior angles of the parallelogram is 30 degrees 

 ,   h = a/2

 A =   b = 1440/a

 P = 2b + 2a = 152cm

0r   b + a = 76

    

     a^2 - 76a + 1440 = 0

  (a-40)(a-36) = 0,  a = 40  0r  a = 36

Parallelogram is 40cm by 36cm



θ	radians	sin θ	cos θ	tan θ

0°	0	0	1	0

30°	π/6	1/2	√3/2	√3/3

45°	π/4	√2/2	√2/2	1

60°	π/3	√3/2	1/2	√3

90°	π/2	1	0	─

 

Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
 Start with what we know about a parallelogram

-  opposite sides are parallel

-  opposite sides are of equal length

-  opposite interior angles are equal (angles "a" are equal, angles "b" are equal)

-  angles "a" and "b" add up to 180 degrees

1) area (A) of parallelogram is the base (b) times the height (h), the perimeter is 2 times (b+s), sin(30) = h/s = 1/2 and s = 2*h 

720 = b*h

152 = 2*(b+s)

substitute for s in second equation

152 = 2*(b+2h)

solve second equation for h, h = (76 - b) / 2

substitute for h in first equation

720 = b * (76 - b) / 2

1440 = 76b - b^2

put equation in standard form

b^2 -76b +1440 = 0

use quadratic formula to solve for b

b = (76+square root(76^2 - 4*1*1440)/(2*1)

b = (76 + 2.45) / 2 =  39.2 cm or

b = (76 - 2.45) / 2 =  36.8 cm

note that h = (76 - 39.2) / 2 = 18.4 cm or

h = (76 - 36.8) / 2 = 19.6 cm

s = 2 * 18.4 = 36.8 cm or

s = 2 * 19.6 = 39.2, therefore

base is 39.2 cm and side is 36.8 cm or

base is 36.8 cm and side is 39.2 cm

2)  we know the area of a circle is equal to pi * radius(r)^2, where r is radius of the base of the statue

area of the bench = 24*pi = pi*(r+2)^2 - pi*r^2

divide both sides of the = by pi

24 = r^2+4r+4 - r^2

24 = 4r +4

4r = 20

r = 5  and

diameter of base of statue = 5 *2 = 10 feet

 









 

RELATED QUESTIONS

Please help me with my Geometry assignment.

here's the problem.

A piece of wire is... (answered by stanbon)

Hi, 

 I need help with this problem: Find the base of a triangle with an area of   15... (answered by checkley75)

hello I need help with my triangle and how to solve it.. The right-angled triangle in the  (answered by ewatrrr)

A parallelogram has an area of 96 cm2 and a height of 4 cm. What is the base length of... (answered by rothauserc)

Can you help me with this assignment in analytic geometry:

Three consecutive vertices... (answered by Edwin McCravy)

Can you please draw and label a parallelogram that has an area of 24 square inches? thank  (answered by AnlytcPhil)

Please help me solve this word problem:

A parallelogram has a base of length 2x+1 and... (answered by checkley71)

I am having difficulty in understatnding these question.  Kindly help me.

1.  A... (answered by mathslover)

Please help me with my assignment for investigating the relationship between the width... (answered by rothauserc)