Question

a piece of stained glass in the shape of a parallelogram LMNO is such that the diagonal LN is at a right angle to LM. Given that LM=12cm and MN=15cm, find the area of the piece of stained glass

Answer 1

the formula of area of rhombus is breadth *height 
b=15cm
h=12cm
area=12*15
=180 square cm.

Answer 2

The area of the piece of stained glass is 180$(cm^{2})$.

Step-by-step explanation:

1. LMNO is a parallelogram. We know in parallelogram opposite side are equal and parallel to each other.

2. So

  MN = LO = 15 (cm)

  ML= NO = 12 (cm)

  $\angle MLN=\angle LNO=90^{\circ}$     (alternate interior angle)

3. Area of LMNO = area of $\Delta MLN$ + area of $\Delta OLN$   ...1)

4. Area of $\Delta MLN$  = $\frac{1}{2}\times MN\times ML=\frac{1}{2}\times 15\times 12=90 (cm^{2})$      ...2)

5.  Area of $\Delta OLN$  =$\frac{1}{2}\times LO\times NO=\frac{1}{2}\times 15\times 12=90 (cm^{2})$      ...3)

6. From equation 1), equation 2) and equation 3)

   Area of LMNO = area of $\Delta MLN$ + area of $\Delta OLN$

  Area of LMNO= 90+90 = 180 $(cm^{2})$