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The sides of square ABCD are extended by sides of equal length to form square WXYZ. If CY = 3 cm and the area of ABCD is 81 sq. cm. Find the area of the four triangles

The sides of square ABCD are extended by sides of equal length to form square WXYZ If CY 3 cm and the area of ABCD is 81 sq cm Find the area of the four triangl class=

Answer :

EliteSoul

Solution :

Given, the sides of square ABCD are extended by sides of equal length to form square WXYZ. If CY = 3 cm and the area of ABCD is 81 cm².

To find : The area of the four triangles.

Here, area of the square ABCD is 81 cm²

We know, area of a square = Side²

So, AB = BC = CD = AD = √(81) cm

→ AB = BC = CD = AD = 9 cm.

Also, AW = BX = DZ = CY = 3 cm [Given]

We can see, ∆AXW , ∆DWZ , ∆CZY , ∆BXY all four triangles are right angled triangles, all having same base and height lengths. So, area of ∆AXW = area of ∆DWZ = area of ∆CZY = area of ∆BXY.

So, area of the 4 triangles = 4 × Area of ∆AXW

→ Area of the 4 triangles = 4 × 1/2 × AW × AX

→ Area of the 4 triangles = [2 × 3 × (AB + BX)] cm²

→ Area of the 4 triangles = [6 × (9 + 3)] cm²

→ Area of the 4 triangles = (6 × 12) cm²

→ Area of the 4 triangles = 72 cm²

Therefore,

Area of the 4 triangles = 72 cm² [Option (iii)]

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