Question

# ∠ABC is a right angle. AB = 8 inches, BC = 13 inches, and AD =...

ABC is a right angle. AB = 8 inches, BC = 13 inches, and AD = 3 feet. Determine the surface area (in square inches) and volume (in cubic inches) of the following. (Round your answers to one decimal place.)

A triangular prism is given. The prism is oriented so that the top and bottom faces are triangles. Four vertices of the prism are labeled as follows:

• The bottom left vertex of the top triangular face is labeled A.
• The top vertex of the top triangular face is labeled B.
• The bottom right vertex of the top triangular face is labeled C.
• The bottom left vertex of the bottom triangular face is labeled D.

surface area in2volume in3

(b)

The base is a square. Determine the surface area (in square feet) and volume (in cubic feet) of the following. (Round your answers to one decimal place.)

120 ft

75 ft

A square pyramid is given. A dashed line that has length 75 ft extends vertically down from the vertex and meets the base at a right angle. The length of one of the bottom edges of the base is 120 ft.

surface area ft2volume ft3

(c)

The diameter is 4 feet 6 inches. The height is 11 feet 3 inches. Determine the surface area (in square feet) and volume (in cubic feet) of the following. (Round your answers to one decimal place.)

A cylinder is given.

surface area ft2volume ft3

Look at the triangular prism shown below. If you were to make a net for this polyhedron, what would be the dimensions of each face? (The triangle is a right triangle.)

3 in.

6 in.

3 in.

A triangular prism is given. The prism is oriented so that the right triangular faces are the front and back faces. Two legs of the triangular face are labeled. The left vertical leg is labeled 3 in. and the bottom horizontal leg is labeled 6 in. The edge that connects the triangle faces is labeled 3 in.

3 in. ✕ 6 in. ✕ 3

 5

in. for each triangular face, 3

 5

in. ✕ 3 in. for the top face, 3 in. ✕ 3 in. for the bottom face, and 3 in. ✕ 3 in. for the remaining vertical face which joins the bottom face and the top edge of the top face3 in. ✕ 6 in. ✕ 45 in. for each triangular face, 45 in. ✕ 3 in. for the top face, 6 in. ✕

 6

in. for the bottom face, and 3 in. ✕ 3 in. for the remaining vertical face which joins the bottom face and the top edge of the top face    3 in. ✕ 6 in. ✕ 3

 5

in. for each triangular face, 3

 5

in. ✕ 3 in. for the top face, 6 in. ✕ 3 in. for the bottom face, and 3 in. ✕ 3 in. for the remaining vertical face which joins the bottom face and the top edge of the top face3 in. ✕ 6 in. ✕ 45 in. for each triangular face, 45 in. ✕ 3 in. for the top face, 3 in. ✕

 6

in. for the bottom face, and 3 in. ✕ 3 in. for the remaining vertical face which joins the bottom face and the top edge of the top face3 in. ✕ 6 in. ✕ 45 in. for each triangular face, 45 in. ✕ 3 in. for the top face, 6 in. ✕ 3 in. for the bottom face, and 3 in. ✕ 3 in. for the remaining vertical face which joins the bottom face and the top edge of the top face

(b)

Look at the figure shown below. If you were to make a net for this polyhedron, what would be the exact dimensions of the "roof"?

2 in.

4 in.

6 in.

A rectangular prism and a half cylinder are given. The front and back faces of the rectangular prism are smaller than the other faces. The figures are oriented so that the rectangular face of the half cylinder is aligned with the top face of the rectangular prism. Three edges of the rectangular prism are labeled as follows.

• The left edge of the front face is labeled 2 in.
• The bottom edge of the front face is labeled 4 in.
• The bottom edge of the right face is labeled 6 in.

4 in. ✕ 3π in.6 in. ✕ π in.    6 in. ✕ 2π in.4 in. ✕ 2 in.2 in. ✕ 3π in.

Determine whether the given information is enough to conclude

ΔABC ≌ ΔDEF.

 (a)

Yes, because the triangles satisfy AAA axiom.No, because AAA is not a congruence axiom for triangles.

 (b)

Yes, because the triangles satisfy the SSS axiom.No, because ACDF so SSS is not satisfied.

 (c) Yes, because the triangles satisfy the SSA axiom.No, because SSA is not a triangle congruence theorem.

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