What is the area of the figure?

Solution:

ABCDE is a composite figure with an equilateral triangle (△ ABC) and a square BCDE.

Given that,

• △ ABC is an equilateral triangle ⇒ AB = BC = CA = 10cm
• BCDE is a square ⇒ BC = CD = DE = BE.

⇒ AB = AC = 10 cm = a (let's say)

Area of the equilateral triangle ABC = (√3/4)a² = (√3/4) × (10)² = (√3/4) × 100 = 25√3 = 43.3 sq. cm

So, area of △ ABC = 43.3 sq. cm

Area of the square BCDE = a² = (10)² = 100 sq. cm

So, area of Square BCDE = 100 sq.cm

Area of the composite figure: area of △ ABC + area of the square BCDE

Total area = (√3/4)a² + a² = 43.3 + 100 = 143.3 sq.cm

Thus, the total area of the given composite figure is 143.3 square centimeters.

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What is the area of the figure?

Summary:

The area of the figure is 143.3 square centimeters.