Area, General Mathematics

Question: The perimeter of a rhombus is 52 metres and its shorter diagonal is twice as long as the other. The length of its diagonal are :
A
12 m

B
18 m

C
10.4 m

D
24 m

Note: side` = (52/4) m = 13 m,` Half of one diagonal = 5 m. Let another diagonal = 2x metre. Then, `x^2 + 5^2 = (13)^2 or x^2 = 144 or x = 12 m.` :. Longer diagonal = 24 m.
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Question: The length of one diagonal of a rhombus is 80% of the other diagonal. The area of the rhombus is how many times the square of the length of the longer diagonal ?
A
`4/5`

B
`2/5`

C
`3/4`

D
`1/4`

Note: Let one diagonal = x cm. Another diagonal `= 80/(100) x` `= (4x)/5 cm.` Area of rhombus` = 1/2 (x xx (4x)/5)` `= 2/5 x^2` `= 2/5` (square of longer diagonal)
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Question: If a square and a rhombus stand on the same base, then the ratio of the areas of the square and the rhombus is :
A
greater than 1

B
equal to 1

C
equal to` 1/2`

D
equal to` 1/4`

Note: A square and a rhombus on the same base are equal in area
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Question: One side of a parallelogram is 18 cm and its distance from the opposite side is 8 cm. The area of the paralleogaram is :
A
`144 cm^2`

B
`72 cm^2`

C
`48 cm^2`

D
`100 cm^2`

Note: Area `= (Base xx height) = (18 xx 8) cm^2` `= 144 cm^2`
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Question: A parallelogram has sides 30 m and 14 m and one of its diagonal is 40 m long. Then, its area is :
A
`336 m^2`

B
`168 m^2`

C
`480 m^2`

D
`372 m^2`

Note: Let ABCD be a 11 gm in which AB = 30 m BC = 14 m & AC = 40 m. Clearly, area of 11 gm ABCD = 2 (area of ABC). Let a = 30, b = 14 & c = 42. Then, `s = 1/2 (a + b + c) = 42` :. Area of
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Question: The two parallel sides of a trapezium are 1.5 m and 2.5 m respectively. If the perpendicular distance between them is 6.5 metres, the area of the trapezium is :
A
`26 m^2`

B
`13 m^2`

C
`20 m^2`

D
`10 m^2`

Note: Area of trap` = 1/2 (Sum of parallel sides xx distance between them)` `= [1/2 (1.5 + 2.5) xx 6.5] m^2` `= 13 m^2`.
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Question: The parallel sides of a trapezium are in the ratio of 3 : 5 and the perpendicular distance between them is 12 cm. If the area of the trapezium is 384 sq. cm, them the smaller of the parallel sides is :
A
16 cm

B
24 cm

C
32 cm

D
40 cm

Note: Let the parallel sides be 3x cm and 5x cm. Then,` 1/2 (3x + 5x) xx 12` `= 384 or x = 8.` :. Smaller of parallel sides = 24 cm
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Question: The cross section of canal is trapezium in shape. The canal is 12 m wide at the top and 8 m wide at the bottom. If the area of the cross section is 840 sq.m, the depth of the canal is :
A
42 m

B
84 m

C
63 m

D
8.75 m

Note: `1/2 (12 + 8) xx d` `= 840 or d = 84 m.`
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Question: The three sides of a triangle are 3 cm, 4 cm and 5 cm respectively. Then, its area (in sq.cm) is :
A
`4sqrt(2)`

B
`2sqrt(3)`

C
`sqrt(23)`

D
6

Note: a = 3, b = 4 and c = 5. `:. s = 1/2 (3 + 4 + 5) = 6` :. Area` = sqrt(6 xx 3 xx 2 xx 1)` `= sqrt(36)` `= 6 sq. cm.`
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Question: The perimeter of an isosceles triangle is 14 cm and the lateral side is to the base in the ratio 5 : 4. The area of the triangle (in sq.cm) is :
A
`sqrt(21)/2`

B
`(3sqrt(21))/2`

C
`2sqrt(21)`

D
`sqrt(21)`

Note: Let the sides be 5x + 5x + 4x = 14 or x = 1. :. sides are 5 cm, 5 cm and 4 cm. `:. s = 1/2 (5 + 5 + 4) = 7. ` :. Area` = sqrt(7 xx 2 xx 2 xx 3)` `= 2sqrt(21) cm.^2` `
1. Report

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Question: The perimeter of a rhombus is 52 metres and its shorter diagonal is twice as long as the other. The length of its diagonal are :

Question: The length of one diagonal of a rhombus is 80% of the other diagonal. The area of the rhombus is how many times the square of the length of the longer diagonal ?

Question: If a square and a rhombus stand on the same base, then the ratio of the areas of the square and the rhombus is :

Question: One side of a parallelogram is 18 cm and its distance from the opposite side is 8 cm. The area of the paralleogaram is :

Question: A parallelogram has sides 30 m and 14 m and one of its diagonal is 40 m long. Then, its area is :

Question: The two parallel sides of a trapezium are 1.5 m and 2.5 m respectively. If the perpendicular distance between them is 6.5 metres, the area of the trapezium is :

Question: The parallel sides of a trapezium are in the ratio of 3 : 5 and the perpendicular distance between them is 12 cm. If the area of the trapezium is 384 sq. cm, them the smaller of the parallel sides is :

Question: The cross section of canal is trapezium in shape. The canal is 12 m wide at the top and 8 m wide at the bottom. If the area of the cross section is 840 sq.m, the depth of the canal is :

Question: The three sides of a triangle are 3 cm, 4 cm and 5 cm respectively. Then, its area (in sq.cm) is :

Question: The perimeter of an isosceles triangle is 14 cm and the lateral side is to the base in the ratio 5 : 4. The area of the triangle (in sq.cm) is :