Question

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

Answer 1

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.

Answer 2

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

$LM^{2} \: + \: LN^{2} \: = \: MN^{2}$

$12^{2} \: + \: LN^{2} \: = \: 15^{2}$

$LN^{2} \: = \: 225\: -\: 144$

$LN \: = \: \sqrt{81}$

$LN \: = \: 9 \: cm$

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 = $\dfrac{1}{2} \times LM \times LN$

Area of Triangle LMN = $\dfrac{1}{2} \times 12 \times 9$

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