Question

What is the area of the colored square?

Answer 1

Answer:

Step-by-step explanation:

Area of each triangle = 1/2 × 5 × 15 = 37.5

Area of 4 triangles = 4 × 37.5 = 150 units

Area of the square = 15 × 15 = 225 units

Area of the coloured square = 225 - 150 = 75 units

Answer 2

Area of square = (side)²

We have to find a length of any square side .

For annotations see  attached figure.

So, In Δ ABC

          ∠ ABC = 90°

          AC = 15

          BC = 5

          If ∠BAC = Ф

          then tan Ф = $\frac{BC}{AC}$

          tan Ф = $\frac{1}{3}$ , sin Ф = $\frac{1}{\sqrt{10} }$ and cos Ф = $\frac{3}{\sqrt{10} }$

         

          Now in Δ DEC, (DE drawn parallel to AB)

          ∠ DEC = 90°

          DC = 10

          ∠ CDE = ∠ BAC = Ф

           So, cos Ф = $\frac{DE}{DC}$

                   $\frac{3}{\sqrt{10} }$ = $\frac{DE}{10}$

              DE = 3$\sqrt{10}$

But DE = GF = 3$\sqrt{10}$

Area of square = (3$\sqrt{10}$)²

Area of square = 90 sq. unit.

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