50

the area of a parallelogram is 120. if the base is reduced to one fourth its original length, and its height is doubled, what is the new area?

a. 30
b. 60
c. 240
d. 120

what is the area of a regular octagon with an apothem 16.9 yards long and a side 14 yards long? rounds the answer to the nearest tenth.

a. 118.3 yd^2
b. 630.9 yd^2
c. 946.4 yd^2
d. 1,892.8 yd^2

find the degree of the central angle for sector c

Answers: 
(1) Option (B) 60.
(2) Option (C) 946.4 yd^2.
(3) Degree of the central angle for sector C = 126°.

Explanations:
(1) The original area of parallelogram is = A = 120

Since
Area-of-parallelogram = (base)(height)
A = bh = 120

Now the base is reduced to one-fourth of its original length and height is doubled. Therefore the new Area will be:


Since bh = 120 (as stated above); therefore:





So the new Area will be 60.

(2) The area of a regular polygon = Area = (1/2)(apothem) (perimeter). 
perimeter = 8 * (side-length) = 8(14) = 112 yards

(8 because it's octagon)
Area =   (1/2)(apothem) (perimeter)Area =   (1/2)(16.9) (112)Area = 946.4 yd^2
(3) For this you need to know the sector-angle formula:

(Area-of-a-given-sector) / (Total Area) = (Degrees-of-the-central-angle)/(Total-degrees)

Area-of-a-given-sector = 0.35
Total Area = 0.35 + 0.15 + 0.5 = 1.0
Degrees-of-the-central-angle = ?
Total Degree = 360°

Plug in the values in equation:
0.35/1 = (Degrees-of-the-central-angle)/360°

=> Degrees-of-the-central-angle = 0.35 * 360° = 126°