Answers:
(1) Option (B) 60.
(2) Option (C) 946.4 yd^2.
(3) D<span>egree of the central angle for sector C = </span>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°
(1) Option (B) 60.
(2) Option (C) 946.4 yd^2.
(3) D<span>egree of the central angle for sector C = </span>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°