What is the area of the figure?
ABCDE is a composite figure with an equilateral triangle (△ ABC) and a square BCDE.
Answer: The area of the figure is 143.3 square centimeters.
Let's find the area of the given composite figure.
- △ 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.