Answer:

A. 442 square units

B. 403 square units

C. 474.5 square units

D. 292.5 square units

Step-by-step explanation:

> Here are the following steps on how to find the Surface Area(SA) of a Right Triangular Pyramid.

1. Firstly, we need to identify the given data and what is missing in the word problem:

• X = 13 units
• Y = 11 units
• Z = 17 units
• Surface Area(SA) = ?

2. Secondly, we need to identify which formula we are going to use to find the Surface Area of the shape:

• Since the shape is a Right Triangular Pyramid and we need to find the Surface Area, then this is the formula we are gonna use:

• SA = BA + LA

1. SA = Surface Area
2. BA = Base Area
3. LA = Lateral Area

3. Thirdly, we need to first find the base area of the pyramid:

• Since the base is a triangle, we need to use this formula to find the base of the pyramid: BA = 1/2 × bh

1. Base = X (13 units)
2. Height = Y (11 units)

• We then next substitute the following to the formula:

1. BA = 1/2 × 13 units × 11 units
2. BA =  71.5 units²

4. Fourthly, we then next find the area of the Lateral Faces:

• Since the 3 lateral faces have the same width and length, we only need to find one area since they all have the same area.
• Like the base, we will use the same formula since the Lateral Faces are also a triangle: LA = 1/2 × bh

1. Base = X (13 units)
2. Height = Z (17 units)

• We then substitute the following to the formula:

1. LA = 1/2 × 13 units × 17 units
2. LA = 110.5 units²

• Since we have three Lateral Faces, we need to add 3 of the same area in the formula since we have 3 lateral faces.

5. Fifthly, after we got the Base Area and Lateral Area, let's substitute them into our formula and solve for the Surface Area:

• Here are the data we obtained:

1. BA =  71.5 units²
2. LA = 110.5 units²

• Let's substitute them into our formula:

1. SA = 71.5 units² + 110.5 units² + 110.5 units² + 110.5 units²
2. SA = 403 units²

6. Finally, we have our answer:

• SA = 403 units²

Other Information:

• A Right Triangular Pyramid is a 3-dimensional triangular pyramid that consists of 4 faces, 6 edges, and 4 vertices.
• A Surface Area is an area occupied by a 3d object by its outer surface.
• An Area is a space occupied by a 2d object or a flat surface.

Learn more about areas:

• What is an Area in math? https://brainly.ph/question/1256354
• What is a Surface Area in math?https://brainly.ph/question/4617591

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