A pedestal for a statue is in the shape of a hexagon formed by a square and two congruent triangles, with the dimensions 7 ft length and 4 feet height. What is the area of the top surface of this pedestal?
a) 19 sq. ft
b) 22 sq ft
c) 25 sq. ft
d) 28 sq, ft
22ft2
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To find the area of the top surface of the pedestal, we need to find the area of the hexagon.
The hexagon is formed by a square and two congruent triangles.
The area of the square can be found by multiplying the length of one side by itself: 7 ft * 7 ft = 49 sq. ft.
The triangles are congruent, so we can find the area of one triangle and then double it.
The formula to find the area of a triangle is 1/2 * base * height. In this case, the base is 7 ft and the height is 4 ft.
Area of one triangle = 1/2 * 7 ft * 4 ft = 14 sq. ft.
Doubling this gives us the total area of the two triangles: 14 sq. ft * 2 = 28 sq. ft.
Adding the area of the square and the two triangles gives us the total area of the hexagon:
49 sq. ft + 28 sq. ft = 77 sq. ft.
Therefore, the area of the top surface of the pedestal is 77 sq. ft, which is not one of the given options.
To find the area of the top surface of the pedestal, we need to find the area of the hexagon. Let's break it down step by step:
1. Start by finding the area of the square portion of the hexagon.
The square has a length of 7 ft and a width of 7 ft, so its area is 7 ft x 7 ft = 49 sq. ft.
2. Next, find the area of one of the congruent triangles.
The height of the triangle is given as 4 ft, and the length of the base (which is also the length of the square) is 7 ft. To find the area of the triangle, we use the formula: Area = (1/2) x base x height.
Plugging in the values, we get: Area = (1/2) x 7 ft x 4 ft = 14 sq. ft.
3. Since there are two congruent triangles in the hexagon, their total area is 2 x 14 sq. ft = 28 sq. ft.
4. Finally, add the area of the square and the area of the two triangles to find the total area of the hexagon: 49 sq. ft + 28 sq. ft = 77 sq. ft.
Therefore, the correct answer is not provided in the options given. The area of the top surface of the pedestal is 77 sq. ft.