Question

IN THE FOLLOWING FIGURES, FIND THE AREA OF THE SHADED PORTIONS:
.
.
.
.
.
.
.
. WHOEVER WILL ANSWER ME CORRECTLY I WILL MARK HIM/HER AS BRILLIANT ✨✨✨✨​

Answer 1

Topic :-

Mensuration

To Find :-

Area of shaded region.

Steps :-

• Calculate area of square.

• Calculate area of remaining three triangles.

• Subtract area of 3 triangles from square.

Solution :-

Calculating area of square

Area of square = ( Side )²

Given side of square = 20 cm

Area of square = ( 20 cm )²

Area of square = 400 cm²

Calculating area of 3 triangles :-

Area of Triangle = ( Base × Height ) / 2

Area of ∆TSU,

• Base = 10 cm
• Height = 10 cm

Area of ∆TSU = [ ( 10 × 10 ) / 2 ] cm²

Area of ∆TSU = 50 cm²

Area of ∆UQR,

• Base = 10 cm
• Height = 20 cm

Area of ∆UQR = [ ( 10 × 20 ) / 2 ] cm²

Area of ∆UQR = 100 cm²

Area of ∆PTQ,

• Base = 10 cm
• Height = 20 cm

Area of ∆PTQ = [ ( 10 × 20 ) / 2 ] cm²

Area of ∆PTQ = 100 cm²

Now,

Area of shaded region = Area of square - Sum of area of 3 triangles

Area of shaded region = 400 cm² - ( 50 + 100 + 100 ) cm²

Area of shaded region = 400 cm² - 250 cm²

Area of shaded region = 150 cm²

Answer :-

So, area of shaded region = 150 cm²

Note :- You may also calculate area of shaded triangle with the help of Heron's Formula after applying Pythagoras Theorem in remaining 3 triangles.

Answer 2

We have to find out area of shaded portion. Which means we have to find out area of ∆QTU.

PQRS is a square of length 20 cm.

➝ area of ∆QTU = Area of square PQRS - [ Area of ∆TSU + Area of ∆PQT + Area of ∆QUR ]

➡️First we will find area of square PQRS :-

=> Area of square PQRS = side× side

= 20×20

= 400 cm²

➡️ Now , we will find area of ∆TSU :-

base = 10 cm

height = 10 cm

Area =( 1/2)× (10)×(10)

= 5 × 10

= 50 cm²

➡️ Now , we will find area of ∆PQT :-

base = 10 cm

height = 20 cm

Area =( 1/2)× (10)×(20)

= 5 × 20

= 100 cm²

➡️ Now , we will find area of ∆QUR :-

base = 10 cm

height = 20 cm

Area =( 1/2)× (10)×(20)

= 5 × 20

= 100 cm²

➝ area of ∆QTU = 400 - [50 + 100 +100 ]

➝ area of ∆QTU = 400 - 250

➝ area of ∆QTU = 150 cm²

Therefore, area of shaded region = 150 cm²