Question

QUESTION :- Find the area of the polygon ABCDEF given alongside if FP = 10 cm, FQ =
20 cm, FR=50 cm, FS = 60 cm and FC = 100 cm. All other measurements are
as given in the figure.

Note: Irrelevant and wrong answers will be reported.
​

Answer 1

Given :-

• FP = 10 cm.
• FQ = 20 cm.
• FR = 50 cm.
• FS = 60 cm.
• FC = 100 cm.
• EP = 40 cm.
• DS = 60 cm.
• AQ = 20 cm.
• SB = 10 cm .

To Find :-

• the area of the polygon ABCDEF ?

Solution :-

in ∆EPF,

→ ∠EPF = 90° .

so,

→ EP = Perpendicular height = 40 cm.

→ FP = Base = 10 cm .

then,

→ Area of ∆EPF = (1/2) * Perpendicular height * Base = (1/2) * 40 * 10 = 200 cm². ----------- (1)

similarly,

in ∆FQA,

→ ∠FQA = 90° .

so,

→ QA = Perpendicular height = 20 cm.

→ FQ = Base = 20 cm .

then,

→ Area of ∆FQA = (1/2) * Perpendicular height * Base = (1/2) * 20 * 20 = 200 cm². ----------- (2)

similarly,

in ∆CSB,

→ ∠CSB = 90° .

so,

→ SB = Perpendicular height = 10 cm.

→ CS = Base = FC - FS = 100 - 60 = 40 cm .

then,

→ Area of ∆CSB = (1/2) * Perpendicular height * Base = (1/2) * 10 * 40 = 200 cm². ----------- (3)

similarly,

in ∆DRC,

→ ∠DRC = 90° .

so,

→ DR = Perpendicular height = 60 cm.

→ RC = Base = FC - FR = 100 - 50 = 50 cm .

then,

→ Area of ∆DRC = (1/2) * Perpendicular height * Base = (1/2) * 60 * 50 = 1500 cm². ----------- (4)

now,

in Trapezium EPRD, we have,

→ EP || DR .

→ PR = Height of Trapezium =>FR - FP = 50 - 10 = 40 cm.

then,

→ Area of Trapezium EPRD = (1/2) * (sum of Parallel sides) * Height = (1/2) * (40 + 60) * 40 = (1/2) * 100 * 40 = 2000 cm². ------------- (5) .

and,

in Trapezium AQSB, we have,

→ AQ || SB .

→ QS = Height of Trapezium =>FS - FQ = 60 - 20 = 40 cm.

then,

→ Area of Trapezium AQSB = (1/2) * (sum of Parallel sides) * Height = (1/2) * (20 + 10) * 40 = (1/2) * 30 * 40 = 600 cm². ------------- (6) .

therefore, adding all six figures we get,

→ Area of Polygon ABCDEF = Area of ∆EPF + Area of ∆FQA + Area of ∆CSB + Area of ∆DRC + Area of Trapezium EPRD + Area of Trapezium AQSB

→ Area of Polygon ABCDEF = 200 + 200 + 200 + 1500 + 2000 + 600 = 4700 cm². (Ans.)

Hence, Area of Polygon ABCDEF will be 4700 cm².

Learn more :-

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