find the area of the figure ABCDEFG as per dimension given it.
ANSWER = 1112.5 cm square.
given answer in process.
Answers
Step-by-step explanation:
Solution :-
Given that
AD = 100 cm
AB = AG = 15 cm
BG = CF = 10 cm
DE = 25 cm
EF = CD = 25 cm
AD = AB + BC + CD = 100 cm
=> 15 + BC + 25 = 100 cm
=> BC + 40 = 100 cm
=> BC = 100-40
=> BC = 60 cm
=> FG = 60 cm
The figure consists of Traingle ,Rectangle and Trapezium.
I) Area of ∆ ABG :-
Base = BG = 10 cm
Height = 15 cm
We know that
Area of a triangle = (1/2) × base × height sq.units
=> Ar(∆ABG) = (1/2)×10×15 cm²
=> Ar(∆ABG) = 5×15 cm²
=> Ar(∆ABG) = 75 cm² ------------(1)
II) Area of the rectangle BCFG :-
Length of the rectangle = BC = GF
= 60 cm
Breadth of the rectangle = BG = CF
= 10 cm
We know that
Area of a rectangle = lb sq.units
Area of the given rectangle
=> BC×BG
=> 60×10 cm²
=>Ar( BCFG) 600 cm² ----------------(2)
III) Area of the Trapezium CDEF:-
Parallel sides of the Trapezium are
CF =(a) = 10 cm
DE = (b) = 25 cm
Distance between two parallel sides
EF = (h) = 25 cm
We know that
Area of a Trapezium = (1/2)h(a+b) sq.units
Area of the given Trapezium
=> (1/2)×25×(10+25) cm²
=> (25/2)×(35) cm²
=> (25×35)/2 cm²
=> 875/2 cm²
=> Ar(CDEF) = 437.5 cm² -----------(3)
Now,
The area of the given figure =
Ar(∆ABG) +Ar( BCFG) + Ar(CDEF)
=> 75+600+437.5 cm²
=> 1112.5 cm²
Answer:-
The total area of the given figure is 1112.5 cm²
Used formulae:-
Area of a triangle :-
Area of a triangle = (1/2) × base × height sq.units
Area of a rectangle :-
Area of a rectangle = lb sq.units
Where, l = length
b = breadth
Area of a Trapezium:-
Area of a Trapezium = (1/2)h(a+b) sq.units
Where, a and b are the Parallel sides of a Trapezium
h = Distance between the two parallel sides