Question

Options are
a) 38 sq. cm
b)26 sq. cm
c)42 sq.cm
d)35 sq.cm

Answer 1

Answer => option - (d) 35cm²

Given :-

• The sides of smaller square which is inside the larger square = 1cm , 2cm, 3cm and 4cm.

• The side of larger square = 11cm

To Find :-

• The area of shaded quadrilateral = ?

Solution :-

To calculate the area of shaded quadrilateral at first calculate the area of 4 smaller square then calculate the area of all rights triangle then add up all their area after we have to subtract the area of larger square and the area of 4 smaller square and the two 4 right angle triangle to calculate the area of shaded quadrilateral. By construction we get 4 right angle triangle and 4 rectangle.

Calculation as per the given attachment:-

• Calculation for all rectangle :-

Area of rectangle OMTL:-

⇢ Area = Length (ML) × Breadth (TL)

⇢ Area = 8 × 1 => 8cm²

Area of rectangle HIJK :-

⇢ Area = Length (IJ) × Breadth (HI)

⇢ Area = 6 × 2 => 12cm²

Area of rectangle EFGS :-

⇢ Area = Length (EF) × Breadth (ES)

⇢ Area = 4 × 3 => 12cm²

Area of rectangle PQNO :-

⇢ Area = Length (PN) × Breadth (PQ)

⇢ Area = 6 × 1 => 6cm²

Calculation for all right angle triangle :-

Area of ∆ OTK :-

⇢ Area = 1/2 × base (TK) × Height (OT)

⇢ Area = 1/2 × 1 × 8 => 4cm²

Area of ∆ KHG :-

⇢ Area = 1/2 × base (HG) × Height (KH)

⇢ Area = 1/2 × 1 × 6 => 3cm²

Area of ∆ GSR :-

⇢ Area = 1/2 × base (SR) × Height (GS)

⇢ Area = 1/2 × 1 × 4 => 2cm²

Area of ∆ OQR :-

⇢ Area = 1/2 × base (QR) × Height (OQ)

⇢ Area = 1/2 × 3 × 6 => 9cm²

Calculation for all smaller square :-

Area of square AERP :-

⇢ Area = Side² (AP)

⇢ Area = 4 × 4 = 16cm²

Area of square FBIG :-

⇢ Area = Side² (BI)

⇢ Area = 3 × 3 => 9cm²

Area of square KJCL :-

⇢ Area = Side² (JC)

⇢ Area = 2 × 2 => 4cm²

Area of square DMNO :-

⇢ Area = Side² (DN)

⇢ Area = 1 × 1 => 1cm²

Now Area of larger square ABCD :-

⇢Area = Side² (AD)

⇢Area = 11 × 11 => 121 cm²

Now sum of Area of all rectangle :-

⇢ Area = 8 + 12 + 12 + 6 => 38cm²

Now sum of all right angle triangle :-

⇢ Area = 4 + 3 + 2 + 9 => 18cm²

Now sum of all smaller square :-

⇢ Area = 16 + 9 + 4 + 1 => 30cm²

Now sum all area which is inside a large square :-

⇢ Area = 38 + 18 + 30 => 86cm²

Now calculate shaded quadrilateral :-

⇢ Shaded Area = Larger square Area - All Area which is inside the larger square

⇢ Shaded Area = 121 - 86 => 35cm²

Hence, the Area of shaded quadrilateral = 35cm²

Answer 2

Answer => option - (d) 35cm²

Solution-

The sides of smaller square which is inside the larger square = 1cm , 2cm, 3cm and 4cm.

The side of larger square = 11cm

To Find :-

The area of shaded quadrilateral = ?

Solution :-

To calculate the area of shaded quadrilateral at first calculate the area of 4 smaller square then calculate the area of all rights triangle then add up all their area after we have to subtract the area of larger square and the area of 4 smaller square and the two 4 right angle triangle to calculate the area of shaded quadrilateral. By construction we get 4 right angle triangle and 4 rectangle.

Calculation as per the given attachment:-

Calculation for all rectangle :-

Area of rectangle OMTL:-

⇢ Area = Length (ML) × Breadth (TL)

⇢ Area = 8 × 1 => 8cm²

Area of rectangle HIJK :-

⇢ Area = Length (IJ) × Breadth (HI)

⇢ Area = 6 × 2 => 12cm²

Area of rectangle EFGS :-

⇢ Area = Length (EF) × Breadth (ES)

⇢ Area = 4 × 3 => 12cm²

Area of rectangle PQNO :-

⇢ Area = Length (PN) × Breadth (PQ)

⇢ Area = 6 × 1 => 6cm²

Calculation for all right angle triangle :-

Area of ∆ OTK :-

⇢ Area = 1/2 × base (TK) × Height (OT)

⇢ Area = 1/2 × 1 × 8 => 4cm²

Area of ∆ KHG :-

⇢ Area = 1/2 × base (HG) × Height (KH)

⇢ Area = 1/2 × 1 × 6 => 3cm²

Area of ∆ GSR :-

⇢ Area = 1/2 × base (SR) × Height (GS)

⇢ Area = 1/2 × 1 × 4 => 2cm²

Area of ∆ OQR :-

⇢ Area = 1/2 × base (QR) × Height (OQ)

⇢ Area = 1/2 × 3 × 6 => 9cm²

Calculation for all smaller square :-

Area of square AERP :-

⇢ Area = Side² (AP)

⇢ Area = 4 × 4 = 16cm²

Area of square FBIG :-

⇢ Area = Side² (BI)

⇢ Area = 3 × 3 => 9cm²

Area of square KJCL :-

⇢ Area = Side² (JC)

⇢ Area = 2 × 2 => 4cm²

Area of square DMNO :-

⇢ Area = Side² (DN)

⇢ Area = 1 × 1 => 1cm²

Now Area of larger square ABCD :-

⇢Area = Side² (AD)

⇢Area = 11 × 11 => 121 cm²

Now sum of Area of all rectangle :-

⇢ Area = 8 + 12 + 12 + 6 => 38cm²

Now sum of all right angle triangle :-

⇢ Area = 4 + 3 + 2 + 9 => 18cm²

Now sum of all smaller square :-

⇢ Area = 16 + 9 + 4 + 1 => 30cm²

sum all area which is inside a large square :-

⇢ Area = 38 + 18 + 30 => 86cm²

Now calculate shaded quadrilateral :-

⇢ Shaded Area = Larger square Area - All Area which is inside the larger square

⇢ Shaded Area = 121 - 86 => 35cm²

the Area of shaded quadrilateral = 35cm²