Area

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181 A parallelogram ABCD has area 48 sqcm. If the length of CD is 8 cm and that of AD is s cm, then which one of the following is necessarily true?

A
s ≥ 6
B
s ≠ 6
C
5 ≤ s ≤ 7
D
s ≤ 6

182 Area of a Rhombus of perimeter 56 cms is 100 sq cms. Find the sum of the lengths of it's diagonals

A
33.40
B
34.40
C
31.20
D
32.30

183 The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar is

A
1300
B
1340
C
1480
D
1520

184 Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is:

A
3√2
B
3
C
4
D
√3

185 Rhombus of side 6 cm has an angle equal to the external angle of a regular octagon. Find the area of the rhombus:

A
18√2 cm2
B
9√2 cm2
C
15√2 cm2
D
12√2 cm2

186 Consider equilateral triangle T inscribed in circle C, what is ratio of the areas of T and C? Consider Circle C inscribed in equilateral triangle T, what is ratio of the areas of T and C?

A
3√3:π , 3√3:16π
B
3√3:4π , 3√3:π
C
√3:π , 3√3:4π
D
√3:π , √3:16π

187 Let ABC be an isosceles triangle. Suppose that the sides AB and AC are equal and let the length of AB be×cm. Let b denote the angle ∠ABC and sin b = 3/5. If the area of the triangle ABC is M square cm, then which of the following is true about M?

A
M < \\frac{x^{2}}{4})
B
M ≥ x2
C
\\frac{3 x^{2}}{4}) ≤ M < x2
D
\\frac{x^{2}}{4}) ≤ M < \\frac{x^{2}}{2})

188 A circle inscribed in a square of side 2 has an equilateral triangle inscribed inside it. What is the ratio of areas of the equilateral triangle to that of the square?

A
9√3 : 16
B
3√3 : 4
C
9√3 : 4
D
3√3 : 16

189 There is an equilateral triangle with a square inscribed inside it. One of the sides of the square lies on a side of the equilateral △. What is the ratio of the area of the square to that of the equilateral triangle?

A
√3 : (5 + 4√3)
B
2√3 : (7 + 4√3)
C
4√3 : (7 + 4√3)
D
4√3 : (5 + 2√3)

190 Consider Square S inscribed in circle C, what is the ratio of the areas of S and C? And, Consider Circle Q inscribed in Square S, what is the ratio of the areas of S and Q?

A
2:π, 4:π
B
4:π, 2:π
C
1:π, 4:π
D
2:π, 1:π