UPSKILL MATH PLUS
Learn Mathematics through our AI based learning portal with the support of our Academic Experts!
Learn moreLet us look at the other two methods of constructing a rhombus.
Method \(3\): When two diagonals are given
Step \(1\): Draw a rough diagram with the known measurements.
Step \(2\): Draw a line segment \(DB\) of \(9\) \(cm\) length.
Step \(3\): Draw a perpendicular line to \(DB\) and mark the intersection as \(O\).
Step \(4\): With \(O\) as centre and with \(4\) \(cm\) as radius, draw two arcs on the perpendicular line and mark the intersections as \(A\) and \(C\) respectively.
Step \(5\): Join \(AD\), \(CD\), \(BC\) and \(AB\) to form the required quadrilateral.
To find the area of the rhombus:
\(\text{Area of the rhombus} = \frac{1}{2} \times d_1 \times d_2\)
\(= \frac{1}{2} \times 9 \times 8\)
\(= 36\) \(cm^2\)
Method \(4\): When one diagonal and one angle is given
Step \(1\): Draw a rough diagram with the known measurements.
Step \(2\): Draw a line segment \(DB\) of \(7\) \(cm\) in length.
Step \(3\): With \(D\) as centre, measure \(50^\circ\) draw a line on both the sides of the line segment.
Step \(4\): Similarly, with \(B\) as centre, measure \(50^\circ\) draw a line on both the sides of the line segment. Mark the intersections as \(A\) and \(C\) to get the desired rhombus.
To find the area of the rhombus:
\(\text{Area of the rhombus} = \frac{1}{2} \times d_1 \times d_2\)
We know that \(DB = 7\) \(cm\). Let \(DB\) be \(d_1\).
To know the length of \(AC\), we should measure the length manually.
When measured, \(AC = d_2 = 5.9\) \(cm\).
\(= \frac{1}{2} \times 7 \times 5.9\)
\(= 20.65\) \(cm^2\)