Question

Find the area of the figure. A composite figure made of a triangle, a square, and a semicircle. The diameter and base measure of the circle and triangle respectively is 6 feet. The triangle has a height of 3 feet. The square has sides measuring 2 feet.

Answer 1

To find the area of the composite figure, we need to calculate the areas of the individual shapes and then sum them up.

Let's start with the triangle:

The base of the triangle is given as 6 feet, and the height is given as 3 feet. The formula for the area of a triangle is A = (1/2) * base * height. Plugging in the values, we get:

• 
  A triangle = (1/2) * 6 ft * 3 ft

= 9 ft²

Next, let's calculate the area of the square:

The side length of the square is given as 2 feet. The formula for the area of a square is A = side length * side length. Plugging in the value, we have:

• 
  A square = 2 ft * 2 ft

= 4 ft²

Now, let's find the area of the semicircle:

The diameter of the semicircle is also given as 6 feet, which means the radius is half of that, so r = 6 ft / 2 = 3 ft. The formula for the area of a semicircle is A = (1/2) * π * r². Plugging in the value, we get:

• 
  A semicircle = (1/2) * π * (3 ft)²

= (1/2) * 3.14 * 3 ft * 3 ft

≈ 14.13 ft²

To find the total area of the composite figure, we add the areas of the individual shapes:

• 
  Total Area = A triangle + A square + A semicircle

= 9 ft² + 4 ft² + 14.13 ft²

≈ 27.13 ft²

Therefore, the approximate area of the composite figure is 27.13 square feet.