Question

please answer with explanation ​

Answer 1

Answer:

area of ABCDE is

=Area of ∆ADE+area of ∆ABF+area of∆CDG

+area of the trapezium BCGF

• AREA OF ∆ADE

$= \frac{1}{2} \times ad \times he \\ = \frac{1}{2} \times 16 \times 5 \: \: cm {}^{2} \\ = 40 \: \: \: cm {}^{2}$

• area of ∆ABF

$= \frac{1}{2} \times af \times bf \\ = \frac{1}{2} \times 4 \times 5 \: \: cm {}^{2} \\ = 10 \: \: cm {}^{2}$

• area of ∆CDG

$= \frac{1}{2} \times cg \times dg \\ = \frac{1}{2} \times 8 \times ((16 - (4 + 6)) \\ = \frac{1}{2} \times 8 \times 6 \\ = 24cm {}^{2}$

• area of trapezium BCGF

$\frac{1}{2} \times fg \times (bf + cg) \\ = \frac{1}{2} \times 6 \times (5 + 8) \\ = 3 \times 13 \\ =39 \: \: cm {}^{2}$

therefore the area of the polygon ABCDE

=(40+10+24+39)cm^2

=113 cm^2

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Answer 2

Step-by-step explanation:

first find out the area of ∆ADE

ar∆ADE=1/2×b×h=1/2×AD×HE

=1/2×16×5. (AD=16, HE=5)

40cm^2

now area ∆AFB =1/2×AF×BF

=1/2×4×5=10

now area of ||gm BFGC=1/2( sum of || side)×( distance between then)

=1/2×(BF+GC)×FG

=1/2×(5+8)×6

=13×6×1/2

=13×3=39

NOW AREA OF ∆CGD=1/2×CG×GD

as AD=AF+FG+GD

16=4+6+GD

16-10=GD=6

∆CGD=1/2×8×6=24

Area Pentagon ABCDE =area∆ADE+ area∆AFB+area||gmBFGC+area ∆CGD

=40+10+39+25=114cm^2