Question

area of the shaded portion. answer 90. explain​

Answer 1

Given :-

• ABCD is a Square.
• All sides are divided in 5, 10.

To Find :-

• Area of Square PQRS .

Formula & Concept Used :-

• Thales Theoram .
• Area of ∆'s is depend upon Their base when Height is same.
• inside angle of Square = 90° .
• Pythagoras Theoram.

Solution ❶ :-

with Basic Method First . Refer To image ⓵ .

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Solution ❷ :-

Lets Try to Solve with Partition Area Method :-

Refer To image ⓶ For Diagram.

From image we can see That :-

Parallelogram DUBW and square PQRS having same height.

So, Base ratio = 10 : 6

Hence, Area ratio = 10 : 6 { Because Height is same }.

so,

☛ 10 unit ---------------------- 150

☛ 6 unit ----------------------- 90 (Ans).

Hence, Area of Square PQRS is 90unit².

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Answer 2

Answer:-

Given:

Side of the big square (ABCD) = (5 + 10) = 15 units.

We know that,

Area of a square = (Side)².

Area of Square ABCD = (15)² = 225 unit².

We observe that, there are four right - angled triangles surrounding the shaded portion .

We know that,

Area of a right angled triangle = ab/2

Area of four right angled triangles = 4(ab/2) = 2ab

Substitute the values,

Area of four right angled triangles = (2*15*4.5) [ The length of DY is being decreased at DS]

Area of four right angled triangles = 135 unit²

Now,

Area of the shaded portion = Area of the big square - Area of four right angled triangles.

Area of the shaded portion = (225 - 135) unit²

Area of the shaded portion = 90 unit².