Question

In a rhombus ABCD, AB=18 and AC=28. Find the area of the rhombus to the nearest tenth.

Answer 1

In a rhombus ABCD , AC  = 28 , AB  = 18.

Diagonals of rambus AC  and BD .

Label the point of intersection of diagonals is X.

The diagonals of a rhombus are perpendicular bisectors of each other.

AX  = XC  = 14. triangle ABX  is a right triangle with hypotenuse 18.

Draw the diagram of the rhombus.

From the pythagoras theorem AB² = AX ² + BX ²

18² = 14² + BX ²

324 = 196 + BX ²

324 - 196 = BX ²

128 = BX ²

BX  = 11.31

Area of ABX  triangle = 1/2(11.31*14) = (158.34)/2 = 79.17

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* 79.17 = 316.68 squre units.

Area of the rhambus = 316.7 square units.