Question

3. Find the area of the pentagonal field shown alongside. All dimensions are in metres.
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Answer 1

Solution :

To find the area of the entire area , let us divide it into various trapezoids and triangles and find their areas seperately !

Area of the pentagonal field :

> Area of ∆ ABC + Area of trapezoid FEDH + Area of triangle DHC + Area of ∆ AGB + Area of ∆ GBC

> ½ × AF × EF + ½ × [ EF + DH ] × [ FH ] + ½ × DH × HC + ½ × AG × GB + ½ × GB × GC

• AF = 40

• EF = 20

• FG = 20

• GH = 30

• DH = 10

• HC = 20

• GB = 40

> ½ × 40 × 20 + ½ × ( 20 + 10) × 50 + ½ × 10 × 20 + ½ × 60 × 40 + ½ × 40 × 50

> 20 × 20 + 15 × 50 + 10 × 10 + 30 × 40 + 20 × 50

> 400 + 750 + 100 + 1200 + 1000

> 3450 Unit² .

This is the required answer.

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Answer 2

Answer:

Area of pentagonal field

=Area of triangle ( ABG+ CDH+ AEF+CGB )+Area of trapezium EFHD

=1/2*40*60+1/2*10*20+1/2*20*40+

1/2*50*40+1/2 (20+10)*50

=1200+100+400+1000+750

=3450 sq. meters

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Here is your answer. .

Hope it will help you. .