Find the area of a rectangular octagon ABCDEFGH having each side equal to
1 cm, HC = 15 cm and AL 1 HC such that AL = 5 cm.
Answers
Answer:
ANSWER
AL=5cm
We know that all sides of regular octagon are equal.
∴ AB=BC=CD=DE=EF=FG=GH=HA=7cm
⇒ HC=GD=15cm
⇒ Area of trapezium ABCH=
2
1
(AH+HC)×AL
=
2
1
(7+15)×5
=
2
1
×22×5
=55cm
2
Area of trapezium ABCH= Area of trapezium GDEF
∴ Area of trapezium GDEF=55cm
2
⇒ Now, are of rectangle HCDG=l×b
=15×7
=105cm
2
⇒ Area of octagon ABCDEFGH= Area of trapezium ABCH+Area of trapezium GDEF+Area of rectangle HCDG
=(55+55+105)cm
2
=215cm²
Answer:
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Step-by-step explanation:
AL=5cm
We know that all sides of regular octagon are equal.
∴ AB=BC=CD=DE=EF=FG=GH=HA=7cm
⇒ HC=GD=15cm
⇒ Area of trapezium ABCH=
2
1
(AH+HC)×AL
=
2
1
(7+15)×5
=
2
1
×22×5
=55cm
2
Area of trapezium ABCH= Area of trapezium GDEF
∴ Area of trapezium GDEF=55cm
2
⇒ Now, are of rectangle HCDG=l×b
=15×7
=105cm
2
⇒ Area of octagon ABCDEFGH= Area of trapezium ABCH+Area of trapezium GDEF+Area of rectangle HCDG
=(55+55+105)cm
2
=215cm
2