ABCD is a quadrilateral in which AB∥DC, and E and F are the mid points of the diagonals AC and BD, respectively. If AB = 14 cm, BC = 64 cm, DC = 72 cm, and AD = 47 cm, then what is the length (in cm) of EF?
29
In a trapezoid with AB parallel to DC, the segment joining the midpoints of the diagonals equals half the difference of the parallel sides: \(EF = \dfrac{|DC-AB|}{2}\).
\(EF = \dfrac{|72-14|}{2} = \dfrac{58}{2} = 29\).
Hence, the length of EF is 29 cm.
Similar Questions
- If one angle of a parallelogram is $18^\circ$ less than twice the smallest angle of the same parallelogram, then the largest angle of the parallelogram is:
- Find the area of a trapezium whose parallel sides are 10 cm and 20 cm and non-parallel sides are equal to 10 cm.
- The angles of a quadrilateral are in the ratios 2 : 4 : 6 : 8. The smallest of these angles is:
- The angles of a quadrilateral are in the ratio of 1 : 3 : 4 : 7. What is the difference between the largest and the smallest angle?
- If ABCD is a cyclic quadrilateral and ABC is an equilateral triangle find the angle of CDA.
- If one angle of a parallelogram is $39^\circ$ less than twice the smallest angle, then the smallest angle of the parallelogram is:
- If one angle of a parallelogram is $30^\circ$ less than twice the measure of the smallest angle, then the measure of the largest angle of the parallelogram is:
- In a rhombus ABCD, if $\angle ACB = 40^\circ, \text{then } \angle ADB = ?$
- P is the mid-point of side BC of a parallelogram ABCD such that $\angle BAP = \angle DAP$.
If AD = 10 cm, then CD = ? - If the angles of a quadrilateral are in the ratio of 4 : 9 : 11 : 12, then the largest of these angles is:
Important Questions from Quadrilaterals
What is the value of AC 2– BD 2
What is the point of intersection of the diagonals?
What is the area of the parallelogram?
ABCD is a cyclic quadrilateral. Diagonals BD and AC intersect each other at E. If ∠BEC = 138° and ∠ECD = 35°, then what is the measure of ∠BAC?
A circle is inscribed in a quadrilateral ABCD, touching sides AB, BC CD and DA at P, Q, R and S, respectively. If AS = 6 cm, BC = 12 cm, and CR = 5 cm, then the length of AB (in cm) is:
