Question

Find the ratio of the areas of the yellow region to the red region in the given figure consisting of right triangles.
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Answer 1

Given:

The figure consisting of right triangles.

To find:

Find the ratio of the areas of the yellow region to the red region in the given figure.

Solution:

From given, we have,

The radius of the circle, r = 7 cm

Area of circle = πr² = 22/7 × 7² = 22 × 7 = 154 cm²

Area of equilateral triangle = √3/4 (s²)

= √3/4 × 14²

= 84.87 cm²

Now compute the value of area of the sector.

Area of sector = ∅/360° × πr²

= 60°/360° × 22/7 × 7²

= 25.66 cm²

Area of shaded region = (Area of circle  + Area of equilateral triangle) - 2 × Area of sector.

Area of shaded region = (154   + 84.87) - 2 × 25.66.

Therefore, the area of the shaded region is 187.55 cm²