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- Question
- 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
- Correct Answer
- 24 cm
ExplanationLet 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. - 1. 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
- 2. 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
- 3. A rectangular carpet has an area of 60 sq. m. Its diagonal and longer side together equal 5 times the shorter side, The length of the carpet is?
Options- A. 5 m
- B. 12 m
- C. 13 m
- D. 14.5 m Discuss
- 4. If D,E and F are respectively the midpoint of the sides BC , CA and AB of a ? ABC and the area of ? ABC = 36m 2. Then area of ? DEF is?
Options- A. 12 cm 2
- B. 9 cm 2
- C. 18 cm2
- D. 19 cm2 Discuss
- 5. Radhika runs along the boundary of a rectangular park at the rate of 12 km/hr and completes one full round in 15 minutes. If the length of the park is 4 times its breadth , the area of the park is?
Options- A. 360000 m2
- B. 360002
- C. 3600 m2
- D. None of these Discuss
- 6. 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
- 7. 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
- 8. 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 Discuss
- 9. 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
- 10. 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
Area problems
Search Results
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: 12 m
Explanation:
Let the longer side = l, shorter side = b and diagonal = d
Then, area of rectangular carpet = l x b = 60 ....(1)
And from question d + l = 5b
? d = 5b - l ...(2)
? d2 = 25b2 + l2 - 10 x lb
? l2+ b2 = 25b2 + l2 - 10 x lb
? l2+b2 = 25b2 + l2 - 10 x 60
? 24b2 = 600
? b = ?25 = 5 m
? l = 60 / b = 60 / 5 = 12 m
Correct Answer: 9 cm 2
Explanation:
Area of a triangle formed by joining the mid point of the sides of the triangle is 1/4th of area of the original triangle .
So area of ? DEF = 36/ 4 = 9 m2
Correct Answer: 360000 m2
Explanation:
Speed = 12 x (5/18) m/sec
=10/3 m/sec
there4; perimeter = (10/3) x 15 x 60 m=3000 m
? 2( a + 4a) = 3000 m
? a = 300 m
So, length = 1200 m and breadth = 300 m
? Area = (1200 x 300 ) m2 = 360000m2
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: 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: 12 cm2
Explanation:
AB = 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
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.
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