Q. If a quadrilateral has sides of lengths 5 cm, 12 cm, 13 cm, and 14 cm, is it a cyclic quadrilateral?
A.
Yes
B.
No
C.
Not enough information
D.
Only if it is a rectangle
Solution
A quadrilateral is cyclic if the sum of opposite angles is 180 degrees. The given side lengths do not provide enough information to determine if it is cyclic.
Q. If the diagonals of a rhombus are 8 cm and 6 cm, what is the area?
A.
24 cm²
B.
48 cm²
C.
36 cm²
D.
30 cm²
Solution
The area of a rhombus can be calculated using the formula (d1 × d2) / 2, where d1 and d2 are the lengths of the diagonals. Here, area = (8 cm × 6 cm) / 2 = 24 cm².
Q. In a rhombus, if one diagonal measures 10 cm and the other measures 24 cm, what is the area?
A.
120 cm²
B.
240 cm²
C.
60 cm²
D.
100 cm²
Solution
The area of a rhombus can be calculated using the formula (d1 * d2) / 2, where d1 and d2 are the lengths of the diagonals. Here, area = (10 cm * 24 cm) / 2 = 120 cm².
Q. What is the length of the diagonal of a rectangle with a length of 8 cm and a width of 6 cm?
A.
10 cm
B.
12 cm
C.
14 cm
D.
16 cm
Solution
The length of the diagonal of a rectangle can be calculated using the Pythagorean theorem: diagonal = √(length² + width²) = √(8² + 6²) = √(64 + 36) = √100 = 10 cm.
