A piece of stained glass in the shape of a parallelogram LMNO IS such that the diagonal LN is aright angle to LM . Given that LM = 12cm and MN = 15cm , find the area of the piece of stained glass
Answers
Answer:
area=180 cm²
Step-by-step explanation:
The formula of area of rhombus is breadth *height
b=15cm
h=12cm
area=12*15
=180 square cm.
Given : LM = 12 cm , MN = 15 cm
LMNO is parallelogram , where LN diagonal is perpendicular to LM.
To Find : Area of the piece of stained glass whose shape is parallelogram.
Solution :
Area of parallelogram = Base × Height
or
Area of parallelogram = 2 × (area of triangle LMN)
(as triangle LON corresponding to LMN)
In triangle LMN ,
By using Pythagorean theorem
By using formula of area of parallelogram
Area = Base × Height
Base = LM = 12 cm
Altitude = LN = 9 cm
Area of LMNO parallelogram = (12 × 9) cm²
Area of LMNO parallelogram = 108 cm²
Or
Area of Triangle LMN =
Area of Triangle LMN =
Area of Triangle LMN = ( 6×9 )cm²
Area of Triangle LMN = 54 cm²
Area of parallelogram LMNO = Twice of area of triangle LMN
Area of parallelogram LMNO = (2 × 54) cm²
Area of parallelogram LMNO = 108 cm²
Answer
Area of stained glass having a shape parallelogram is 108 square cm.
Note : For your reference diagram is attached in a image