Question

12. There is a pentagonal park. Its area is found in two different ways.Are they same?​

Answer 1

Answer:

refer to the image for answer

Step-by-step explanation:

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Answer 2

Answer:

Yes the area using both the methods are same.

Step-by-step explanation:

ᴍᴇᴛʜᴏᴅ ɪ :

Following the figure, there are two trapezium which combines to form a pentagonal park.

Here, the dimensions of the trapezium will be :

• h (height) = 10cm.
• a = 20cm.
• b = 30cm.

Area of the trapezium is given by :

→ ½ · (a + b) · h

→ ½ · (20 + 30) · 10

→ ½ · (50) · 10

→ ½ · 500

→ 250cm²

Since, the figure is having two trapezium equal.

Therefore,the area of the figure ɪ is :

→ 250 + 250

→ 500cm²

ᴍᴇᴛʜᴏᴅ ɪɪ :

The second figure, is split into :

• A triangle and a square.

Dimensions of the square :

each side = 20cm.

Area of the square is given by :

→ (each side)²

→ (20)²

→ 400cm²

Find the area of the △:

Dimensions of the triangle :

• base = 20cm.
• height = 10cm.

Area of the triangle is given by :

→ ½ · base · height

→ ½ · 20 · 10

→ ½ · 200

→ 100cm²

Area of the figure :

→ area of the square + area of the △

→ (400 + 100)cm²

→ 500cm²

Hence, the area of using both methods gives the same.