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- Question
- The adjacent sides of parallelogram are 6 cm and 4 cm and the angle between then is 30°. The area of the parallelogram is?
Options- A. 12 cm2
- B. 24 cm2
- C. 48 cm2
- D. None of these
- Correct Answer
- 12 cm2
ExplanationAB = 6 cm ; AD = 4 cm and ? BAD = 30°
Area of parallelogram ABCD = AB x AD x sin 30°
= 6 x 4 x sin 30° = 12 cm2 - 1. A parallelogram has sides 60 m and 40 m and one of the diagonal is 80 m long. Then its area is?
Options- A. 480 sq. m
- B. 320 sq. m
- C. 600? 15 sq. m
- D. 450 ? 15 sq. m Discuss
- 2. The two parallel sides of a trapezium are 1 meters and 2 meters respectively . The perpendicular distance between them is 6 meters. The area of the trapezium is?
Options- A. 18 sq. meters .
- B. 12 sq. meters .
- C. 9 sq. meters .
- D. 6 sq. meters . Discuss
- 3. The area of a trapezium is 384 sq.cm. If its parallel sides in ratio 3 : 5 and the perpendicular distance between them be 12 cm. The smaller of parallel sides is?
Options- A. 16 cm
- B. 24 cm
- C. 32 cm
- D. 40 cm Discuss
- 4. The cross section of a canal is a trapezium in shape . If the canal is a trapezium in shape. If the canal is 10 meters wide at the top and 6 meters wide at bottom and the area of cross section is 640 sq. meters The depth of canal is?
Options- A. 40 meters
- B. 80 meters
- C. 160 meters
- D. 384 meters Discuss
- 5. In ? ABC ,sides BC = 10 cm and height AD = 4.4 cm. If AC = 11 cm. Then altitude BE equals?
Options- A. 5 cm
- B. 4 cm
- C. 5.6 cm
- D. 5.5 cm Discuss
- 6. One side of a parallelogram is 14 cm. Its distance from the opposite side is 16 cm. The area of the parallelogram is?
Options- A. 112 sq. cm
- B. 224 sq. cm
- C. 56? sq. cm
- D. 210 sq. cm Discuss
- 7. The length of the diagonal of a rhombus is 80% of the length of the other diagonal, Then the area of the rhombus is how many times the square of the length of the longer diagonal?
Options- A. 4/5
- B. 2/5
- C. 3/4
- D. 1/4 Discuss
- 8. In a rhombus, whose area is 144 sq.cmone of its diagonal is twice as long as the other, The lengths of its diagonals are?
Options- A. 24 cm, 48 cm
- B. 12 cm, 24 cm
- C. 6 ?2 cm, 12?2 cm
- D. 6 cm, 12 cm Discuss
- 9. The lengths of three line segments (in cm) are given in each of the four cases. Which one of the following cases is not suitable to be the three sides of a triangle?
Options- A. 2, 3, 4
- B. 2, 3, 5
- C. 2, 4, 5
- D. 3, 4, 5 Discuss
- 10. The three sides of a triangle are 15, 25 and x units. Which one of the following is correct?
Options- A. 10< x < 40
- B. 10? x ? 40
- C. 10 ? x < 40
- D. 10 < x ? 40 Discuss
Area problems
Search Results
Correct Answer: 600? 15 sq. m
Explanation:
AB = 60 m, BC = 40 m and AC = 80 m
? s = (60 + 40 + 80 ) / 2 m = 90 m
(s-a) = 90 - 60 = 30 m,
(s-b) = 90 - 40 = 50 m and
(s-c) = 90 - 80 = 10 m
? Area of ? ABC =
?s(s-a)(s-b)(s-c)
= ?90 x 30 x 50 x 10 m2
= 300?15 m2
? Area of parallelogram ABCD = 2 x area of ? ABC
= 600?15 m2
Correct Answer: 9 sq. meters .
Explanation:
Area of trapezium = 1/2 x sum of parallel sides x perpendicular distance between them
= 1/2 (1 + 2) x 6 m2
= 9 m2
Correct Answer: 24 cm
Explanation:
Let the parallel sides be 3a and 5a.
So Area of trapezium = 1/2 x sum of parallel side x perpendicular distance between them.
? 1/2 (3a +5a) x 12 = 384
? 8a = 64
? a =8
? Smaller side = 3x = 3 x 8 = 24 cm.
Correct Answer: 80 meters
Explanation:
Cross section area = 1/2 x ( a + b ) x d
where a and b are the parallel sides, d is the perpendicular distance between them.
? 1/2 x ( a + b ) x d = 640
? d = (640 x 2) / 16 = 80m
Correct Answer: 4 cm
Explanation:
We know that area of triangle = ( base x height ) / 2
So area of triangle = (BC x AD) / 2 = (AC x BE) / 2
? (10 x 4.4) / 2 = (11 x h) / 2
? h= (10 x 4.4)/11 = 4 cm
Correct Answer: 224 sq. cm
Explanation:
Area of parallelogram = Side of parallelogram x distance from the opposite side
= 14 x 16 cm2
= 224 cm2
Correct Answer: 2/5
Explanation:
Let length of the longer diagonal = d cm
Then, length of other diagonal = 0.8 x d cm
Area of rhombus = (1/2) x d x 0.8 x d = 2/5 d2
= 2/5 d2
Area of square of the length of the longer diagonal = d2
So the area of the rhombus is 2/5 times the square of the length of the longer diagonal.
Correct Answer: 12 cm, 24 cm
Explanation:
Area of rhombus = (d1 x d2) / 2
? (d x 2d ) / 2 = 144
? d2 = 144
? d = 12
? Length of diagonal = 12 cm, 24 cm
Correct Answer: 2, 3, 5
Explanation:
We know that in any triangle
"the sum of two sides is always greater than its third side" and
"the difference of two sides is always less than its third side".
(i) 2 + 3 is not greater than 5
(ii) |5 - 2| not less than 3
Correct Answer: 10< x < 40
Explanation:
In a triangle
Sum of two sides is always greater than 3rd side
i.e., x < 25 + 15 = 40 .....(i)
Difference of two sides is always less than 3rd side
i.e., 25 - 15 = 10 < x ...(ii)
From Eqs. (i) and (ii) , we get
10 < x < 40
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