ABCD is a square with a side length of 3. E and F are the midpoints of sides AB and BC, respectively. What is the area of the quadrilateral EBFD?

Given : - Square ABCD with side 3. E and F as midpoints. To find : - area of EBFD
Solution : - We have, area of square ABCD = 3 x 3 = 9 units.
Thus, (ar)EBFD = ar ABCD - ar DAE - arDCF
arDAE = 1/2 x base x height
=1/2 x 1.5 x 3 ( AE is 1/2 of AB = 1.5, DA is altitude) = 2.25
arDFC = 1/2 x base x height = 1/2 x 1.5 x 3 (FC is 1/2 of BC, DC is altitude) = 2.25
Thus, (ar) EBFD = arABCD - arDAE - arDCF
= 9 - 2.25 - 2.25
= 4.5 units.
Thus, area of quad EBFD is 4.5 units.

Answered by tadvisohil886 | 2024-06-10

The area of quadrilateral EBFD can be calculated using the coordinates of its vertices and the Shoelace formula. After applying the formula, we find that the area is 4.5 square units. Hence, EBFD has an area of 4.5 square units.
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Answered by tadvisohil886 | 2024-12-24