the complete question in the attached figure
we know
In a rhombus ABCD
, AC
= 26 , AB
= 14
the diagonals of a rhombus are perpendicular bisectors of each other
AX
= XC
= 13. triangle ABX
is a right triangle with hypotenuse 14.
From the pythagoras theorem AB² = AX² + BX²
14² = 13² + BX²
196 = 169 + BX²
27 = BX²----- > BX=√27
BX = 5.20
Area of ABX
triangle=(1/2)*5.2*13=33.77
The four triangles formed by construction of the diagonals are all congruent since the diagonals are perpendicular bisectors.
Total area of the rhombus is 4 times of ABX triangle
Area = 4* 33.77=135.10 units²
the answer is the option D) 135.1 units ²
