Question

In the following figure find the area of the shaded ​

Answer 1

Answer:

calculate the perimeter and then the formula .

Step-by-step explanation:

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Answer 2

Answer:

• SU = 10 cm
• UR = 10 cm
• QR = 20 cm
• ST = 10 cm
• PT = PS - ST = QR - ST = 20 - 10 = 10 cm
• PQ = SR = 20 cm

We can see that each side is equal to 20 cm, hence it is a Square.

We know the property of Square that each side is equal to 90°, It will form three right angle triangle QRU, TSU and QPT.

• Area of different right angle triangles :

⇒ Ar. QRU = ½ × UR × QR

⇒ Ar. QRU = ½ × 10 × 20

⇒ Ar. QRU = 10 × 10

⇒ Ar. QRU = 100 cm²

⇒ Ar. TSU = ½ × SU × TS

⇒ Ar. TSU = ½ × 10 × 10

⇒ Ar. TSU = 5 × 10

⇒ Ar. TSU = 50 cm²

⇒ Ar. QPT = ½ × PQ × PT

⇒ Ar. QPT = ½ × 20 × 10

⇒ Ar. QPT = 10 × 10

⇒ Ar. QPT = 100 cm²

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• Area of Shaded region :

⇢ Ar. QTU = Ar. PQRS - (Ar. QRU + Ar. TSU + Ar. QPT)

⇢ Ar. QTU = (20 cm)² - (100 + 50 + 100) cm²

⇢ Ar. QTU = 400 cm² - 250 cm²

⇢ Ar. QTU = 150 cm²

∴ Hence, area of shaded region is 150 cm².