A collage is made up of 400 rhombus shaped pieces and 200 trapezium shaped pieces. The diagonals of the rhombus are 6cm and 4 cm long. The lengths of the parallel sides of the trapezium are 4cm and 8cm , and height is 10cm. Find the area of the collage and also the cost of painting it at the rate of Rs. 250 per sq. m.
Answers
Answer:
Area of the collage = 16800 sq.cm or 1.68 sq.m
Total cost of painting the collage =Rs.420
Step-by-step explanation:
Given:-
A collage is made up of 400 rhombus shaped pieces and 200 trapezium shaped pieces. The diagonals of the rhombus are 6cm and 4 cm long. The lengths of the parallel sides of the trapezium are 4cm and 8cm , and height is 10cm.
To find:-
Find the area of the collage and also the cost of painting it at the rate of Rs. 250 per sq. m.
Solution:-
Given collage is made up of rhombus shaped pieces and Trapezium shaped pieces.
Diagonals of rhombus=6cm and 4cm
Let d1=6cm
d2=4cm
Area of Rhombus=(d1×d2)/2sq.units
Area of rhombus=(6×4)/2 sq.cm
Area of rhombus=6×2 sq.cm
Area of rhombus=12 sq.cm
Total number of rhombus pieces=400
Total area of all rhombus pieces
=400×12=4800 sq.cm--------------------(1)
The lengths of the parallel sides of the trapezium are 4cm and 8cm
Let a=4cm
b=8cm
height =(h)=10cm.
Area of Trapezium=h(a+b)/2 sq.units
Area of Trapezium=10(4+8)/2 sq.cm
Area of Trapezium=10(12)/2 sq.cm
Area of Trapezium=10×6 sq.cm
Area of Trapezium=60 sq.cm
Number of all Trapezium pieces=200
Total area of all Trapezium pieces
=200×60
=12000 sq.cm---------------------------(2)
Total area of the collage=Area of all rhombus pieces+Area of all Trapezium pieces
=>Total area of collage=4800+12000
=>Total area of the collage =16800 sq.cm
we know that 10000 sq.cm=1 sq.m
16800 sq.cm=16800/10000=1.68 sq.m
The cost of painting the collage per 1 sq.m
=Rs.250
The cost of Painting the collage of 1.68 sq.m
=1.68×Rs.250
=Rs.420
Using Concept:-
Total area of the collage=Area of all rhombus pieces+Area of all Trapezium pieces.
Using formulae:-
- Area of Rhombus=d1×d2/2 sq.units
- Here, d1 and d2 are the diagonals of the rhombus.
- Area of Trapezium=h(a+b)/2 sq.units
- Here, a and b are the parallel sides and h is the height of the Trapezium.