Quadrilaterals

Q. A quadrilateral has sides of lengths 5 cm, 12 cm, 13 cm, and 14 cm. Is it a cyclic quadrilateral?

Solution

A quadrilateral is cyclic if the sum of opposite angles is 180 degrees. This cannot be determined with just side lengths.

Correct Answer: B — No

Q. A trapezium has bases of lengths 8 cm and 12 cm, and the height is 5 cm. What is the area of the trapezium?

Solution

Area = 1/2 * (base1 + base2) * height = 1/2 * (8 + 12) * 5 = 50 cm².

Correct Answer: B — 60 cm²

Q. If a quadrilateral has sides of lengths 6 cm, 8 cm, 10 cm, and 12 cm, can it form a valid quadrilateral?

Solution

A quadrilateral can be formed if the sum of any three sides is greater than the fourth side. Here, it is valid.

Correct Answer: A — Yes

Q. If the lengths of the diagonals of a rectangle are 10 cm and 24 cm, what is the perimeter of the rectangle?

Solution

Using the Pythagorean theorem, the sides are 10 cm and 24 cm. The perimeter is 2(10 + 24) = 68 cm.

Correct Answer: A — 68 cm

Q. In a parallelogram, if one angle is 70 degrees, what are the measures of the other three angles?

Solution

In a parallelogram, opposite angles are equal and adjacent angles are supplementary. Thus, the angles are 70, 110, 70, 110.

Correct Answer: B — 70, 70, 110

Q. In a square, if the length of one side is doubled, what happens to the area?

Solution

If the side length is doubled, the area increases by a factor of 4 (since area = side²).

Correct Answer: D — It quadruples

Q. The diagonals of a rhombus bisect each other at right angles. If one diagonal is 10 cm long, what is the length of each half?

Solution

Each half of the diagonal is 10 cm / 2 = 5 cm.

Correct Answer: B — 5 cm

Q. What is the area of a quadrilateral with vertices at (0,0), (4,0), (4,3), and (0,3)?

Solution

The area is length * width = 4 * 3 = 12.

Correct Answer: A — 12

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