Diagram of the adjacent picture frame has outer dimensions 28cm × 24cm and inner dimensions 20cm × 16cm. Find the area of shaded part of frame , if width of each section is the same.
Note :- Picture is in attachment.
Answers
Step-by-step explanation:
Given:-
Diagram of the adjacent picture frame has outer dimensions 28cm × 24cm and inner dimensions 20cm × 16cm.
To find:-
Find the area of shaded part of frame , if width of each section is the same.
Solution:-
From the figure we have,
Outer dimensions of the frame are 28 cm and 24 cm
Inner dimensions of the frame are 20 cm and 16 cm
Let the Width of the frame be w cm
Given tht
width of each section is the same.
Then Outer dimension of frame
= inner dimension+ 2w
=> 24 = 16+2w
=> 24-16 = 2w
=> 2w = 8
=> w = 8/2
=> w = 4 cm
width = Perpendicular distance between the length of the outer and inner frames of the shaded part
Let h = 4 cm
The shaded region is like a Trapezium
Area of the shaded region = Area of the trapezium = (1/2)×h(a+b) sq.units
We have
h = 4 cm
a = 28 cm
b= 20 cm
Area of the shaded region
=> (1/2)×4(28+20) sq.cm
=> (4/2)×(48) sq.cm
=> 2×48 sq.cm
=> 96 sq.cm
Answer:-
The area of shaded part of frame is 96 sq.cm
Used formula:-
Area of the trapezium = (1/2)×h(a+b) sq.units
Where, a and b are the Parallel sides and h is the perpendicular distance between them
Given:
outer dimensions 28 cm×24 cm and inner dimensions 20 cm×16 cm
Area of shaded region =(areaEFJI−areaEFGH)+ 2 × area △AIH
= (20×20−16×20)+2×21×4×4
= (400−320)+16=80+16= 96