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In the following figure, the only reflex angle of the dart is 216° and the second largest angle is 72°. If each of the two smaller sides is 1 cm and each of the two larger sides is (1+5)2, find the area of the dart, in sq. cm.

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Important Questions on Geometry

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Quantum CAT Also Useful for XAT>Chapter 12 - SNAP>CMAT>Q 84

In the following quadrilateral ABCD, the four mid-points P, Q, R, S are joined in such a way that the quadrilateral is divided into six parts.

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The ratio of the quadrilaterals  □ASOP□POQB, □OORCQ □ SDRO is 4: 5: 7: 6 and the ratio of ∆ASP and ∆RCQ is 2: 5. If S is joined to R and P is joined to Q, find the ratio of □PQRS and □ABCD.

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Quantum CAT Also Useful for XAT>Chapter 12 - SNAP>CMAT>Q 85
In a rhombus ABCD,∠ADC:∠BCD=1:2 and EF: BD=1: 3, where E and F lie on the diagonal BD, inside the rhombus, such that □AECF is a quadrilateral. Find the ratio of areas of □AECF:□ABCD.
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Quantum CAT Also Useful for XAT>Chapter 12 - SNAP>CMAT>Q 86
An isosceles trapezium whose parallel sides are in the ratio 1: 4. It inscribes a circle that touches all the sides of the trapezium. If the sum of the two parallel sides is 70 cm, find the circumference of the inscribed circle.
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Quantum CAT Also Useful for XAT>Chapter 12 - SNAP>CMAT>Q 87
A 7×24 rectangular thin wall has a 2×2 square shaped window in such a way that the intersection of diagonals of rectangle and the intersection of diagonals of square coincide with each other. Which one of the following is correct?
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Quantum CAT Also Useful for XAT>Chapter 12 - SNAP>CMAT>Q 88
A trapezium inscribes a circle that touches all its sides and the line connecting the mid-points of the non-parallel sides of the trapezium divides the trapezium in such a way that the area of one part is half the area of the other part. If the lengths of the non-parallel sides be 8 cm and 16 cm, find the length of the shortest side of the trapezium.
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Quantum CAT Also Useful for XAT>Chapter 12 - SNAP>CMAT>Q 89
A point O lies inside a square ABCD such that OA=3, OB=4 and OD=5, find the value of OC.
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Quantum CAT Also Useful for XAT>Chapter 12 - SNAP>CMAT>Q 90
In a ∆ABC,CP and BQ intersect each other at R inside the triangle, where P and Q lie on the sides AB and AC respectively. ∠BAC=50°,∠ABC=70°,∠ACB=∠APQ and PC=BC. Find ∠PBQ.
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Quantum CAT Also Useful for XAT>Chapter 12 - SNAP>CMAT>Q 91
Which of the following statements is/are correct?
(i) A kite always has two axes of symmetry
(ii) A square is both a kite and an isosceles trapezium
(iii) Every kite is an orthodiagonal
(iv) An isosceles trapezium can have a circumcircle
(v) A kite can always have an incircle
(vi) If the sum of two opposite sides is not the same as the sum of the other pair of opposite sides, it can never be a circumscribing quadrilateral.