Math, asked by dhritivoggu7, 1 month ago

Find the area of the shaded region in the following figure.

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Answers

Answered by chocogirl520
1

Answer:

106cm²

Step-by-step explanation:

the side cm is 10 cm the other side is 6 cm and the cube represent 90cm so in total

10cm + 6cm+ 90 cm = 106cm

hope it will help you

Answered by whamwham
3

Important Formulae

Area of a rectangle: length × breath

Area of a triangle: 1/2 × base × height

Pythagoras theorem: the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the sides.

Answer

  • Finding the area of rectangle PQRS

We know that:

⇒ Area of a rectangle = length x breath

⇒ Area of PQRS = 14 cm x 10 cm

                            = 140 cm²

  • Finding TC

In order to find the area of ΔTCR, we need to know both the base (given) and the height (not given). As this is a right-angled triangle, we can find TC using the Pythagoras Theorem:

⇒ s² + s² = h²

⇒ RT² + TC² = CR²

⇒ 6² + TC² = 10²

⇒ TC² = 10² - 6²

⇒ TC² = 100 - 36

⇒ TC² = 64

⇒ TC = 8 cm

  • Finding the area of ΔTCR

Here, base = TR = 6 cm

         height = TC = 8 cm

We know that:

⇒ Area of a triangle = 1/2 × base × height

⇒ Area of TCR = 1/2 × 6 × 8

                         = 6 × 4

                         = 24 cm²

  • Finding the area of the shaded portion

The area of the shaded portion is:

⇒ Area of rectangle - area of triangle

⇒ 140 cm - 24 cm

⇒ 116 cm²

Therefore, the area of the shaded region is 116 cm².

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