Respuesta :
The surface area of the composite figure is 333 sq. in.
The correct answer is an option (2) 333 in²
What is a pyramid?
"It is a three-dimensional geometric shape with a polygon as its base and the lateral surfaces as triangles which meet at a common point."
What is rectangular prism?
"It is a three-dimensional geometric structure which has six faces that are rectangles."
What is a composite figure?
"A figure that consists of two or more geometric shapes."
Area of rectangle:
A = length × width
Area of the triangle:
A = 1/2 × base × height
For given example,
A rectangular prism and a square pyramid were joined to form a composite figure.
The composite figure would have nine faces with four triangular faces and five rectangular faces.
Surface area of the composite figure would be the sum of surface area of all nine faces.
The dimensions of the rectangular base the composite figure are length of 9 inches, width of 9 inches.
Using the formula for an area of the rectangle,
⇒ A1 = 9 × 9
⇒ A1 = 81 square inches
The surface area of the larger vertical rectangular faces is same.
So, A2 = 2 × (area of the larger vertical rectangular faces)
The dimensions of the larger vertical rectangular faces 9 inches × 5 inches.
⇒ A2 = 2 × (9 × 5)
⇒ A2 = 2 × 45
⇒ A2 = 90 square inches
Similarly, the surface area of the smaller vertical rectangular faces is same.
So, A3 = 2 × (area of the smaller vertical rectangular faces)
The dimensions of the smaller vertical rectangular faces 9 inches × 5 inches
⇒ A3 = 2 × (9 × 5)
⇒ A3 = 2 × 45
⇒ A3 = 90 square inches
The four triangular faces are identical.
Let A4 be the total surface area of four triangular faces.
⇒ A4 = 4 × (area of triangular face)
⇒ A4 = 4 × (1/2 × base × height)
⇒ A4 = 4 × (1/2 × 9 × 4)
⇒ A4 = 4 × 18
⇒ A4 = 72 square inches
So, the surface area of the composite figure is,
⇒ A = A1 + A2 + A3 + A4
⇒ A = 81 + 90 + 90 + 72
⇒ A = 333 sq. in.
Therefore, the surface area of the composite figure is 333 sq. in.
The correct answer is an option (2) 333 in²
Learn more about pyramid and rectangular prism here:
brainly.com/question/24046619
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