Question
In a cyclic quadrilateral, the diagonals intersect at an
angle of 60°. If the sides of the quadrilateral are 6 cm, 8 cm, 10 cm, and 12 cm, what is the area of the quadrilateral?Solution
The area of a cyclic quadrilateral can be calculated using formula: Area = √[(s - a)(s - b)(s - c)(s - d)], where s = (a + b + c + d) / 2. Here, s = (6 + 8 + 10 + 12) / 2 = 18 cm. Area = √[(18 - 6)(18 - 8)(18 - 10)(18 - 12)] = √[12 × 10 × 8 × 6] = √5760 = 75.89 cm² ≈ 76 cm². Correct answer: c) 76 cm²
Out of their respective monthly salaries, Soma spends 7/8 and Tina spends 4/5 on various expenses. The salary remaining with Tina after the expenses is ...
A, B, and C invested Rs. 4800, Rs. 3200, and Rs. x, respectively, in a business for equal time. If the profit received by C is Rs. 1500 out of a total p...
‘K’ and ‘L’ formed a business investing in the ratio 8:7 for 3 years. They decide to give 12% of the profit to a community development fund. If ...
In a business there are two partners ‘P’ and ‘Q’. ‘P’ started the business with the capital of Rs. 24000 and after 3 months ‘Q’ joined h...
A, B and C invested in partnership. A invest Rs.12000 for 5 months, B invests Rs.8000 for 3 months and C invests Rs.15000 for 2 months. C is working par...
M and N invested Rs. 3200 and Rs. 4800 respectively. After 15 months, M raised his investment by 25% and N decreased his by Rs. 800. If total profit aft...
Three partners, R, S, and K, form a partnership business with capitals in the ratio of 3:5:8. After four months, R, S, and K added Rs. 3000, Rs. 4500, a...
P and Q together started a business with initial investment in the ratio of 1:5, respectively. The time-period of investment for P and Q is in the ratio...
‘A’ and ‘B’ invested Rs. 4800 and Rs. 3600, respectively in a business, together. After 6 months, ‘A’ withdrew 25% of his initial investment...
‘A’ and ‘B’ invested Rs. 4800 and Rs. 3200, respectively in a business, together. After 6 months, ‘A’ withdrew 35% of his initial investment...
