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In a trapezium ABCD, AB and DC are parallel sides and ∠ADC = 90°. If AB = 15 cm, CD = 40 cm and diagonal AC = 41 cm. then the area of the trapezium ABCD is
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- 245 cm.²
- 240 cm.²
- 247.5 cm.²
- 250 cm.²
- 245 cm.²
Correct Option: C
∠ADC = 90°
AC = 41 cm.
CD = 40 cm.
∴ AD = √AC² -CD²
= √41² - 40²
= √(41 + 40)(41 - 40)
= √81 = 9 cm.
∴ Area of trapezium ABCD
| = | (AB + CD) × AD | |
| 2 |
| = | (15 + 40) × 9 | |
| 2 |
=
| = | × 55 × 9 | |
| 2 |
= 247.5 sq. cm.
