Question

A) Identify the cross section of each figure. (6 points)
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Question 2

How many faces does this shape have? faces
Area of the Left Side = square inches
A)
7th Grade Math Formula Sheet
Consider the three-dimensional below.
Determine the total surface area of the figure. The formula chart is at the bottom of the page.
(5 points)

Area of the Back = square inches
Area of the Bottom = square inches
TOTAL surface area of the figure = square inches

Question 3

How many faces does this figure have? faces
Area of each triangular face = square centimeters
A)
7th Grade Math Formula Sheet
Consider the figure below.
Determine the total surface area of the triangular prism. The formula chart is at the bottom of the page.
(6 points)

Area of the smallest rectangular face = square centimeters
Area of the middle rectangular face = square centimeters
Area of the largest rectangular face = square centimeters
TOTAL Surface Area of the Triangular Prism = square centimeters

Answer 1

I can’t see the figures in your message. Please upload the images (or type the dimensions and how the plane cuts each solid) and I’ll give exact answers. Meanwhile, here are the rules, formulas, and step-by-step templates you can use to finish each part.

A) Identifying cross-sections — quick rules
- For a prism (base is a polygon):
- A plane parallel to the base → cross-section = same polygon as the base.
- A plane perpendicular to the base and cutting through the lateral faces → cross-section = rectangle.
- For a rectangular prism / cube:
- Plane parallel to a face → rectangle (or square).
- Plane perpendicular to a face and cutting across → rectangle (may be square).
- A diagonal cut can produce a triangle, rectangle, or hexagon depending on the plane.
- For a cylinder:
- Plane perpendicular to axis → circle.
- Plane parallel to axis → rectangle (in the net; in 3D the intersection is a rectangle “strip” unwrapped — usually an ellipse if oblique).
- Oblique cut → ellipse.
- For a cone:
- Plane perpendicular to axis → circle.
- Oblique plane not through base → ellipse.
- Plane through the apex → triangle (in cross-section).
- For a pyramid:
- Plane parallel to base → similar polygon (smaller).
- Plane through apex → triangle.

Use these to identify each cross-section once you tell me the orientation of the cutting plane for each figure.

Question 2 (rectangular prism style) — how to compute
1. Count faces: rectangular prism has 6 faces.
2. Areas (use labeled dimensions; common labels: width = w, height = h, depth = d)
- Left side area = height × depth = h × d
- Back area = height × width = h × w
- Bottom area = width × depth = w × d
3. Total surface area = 2*(w·h + h·d + w·d)
Fill in the specific w,h,d from your figure and compute each face area, then add.

Question 3 (triangular prism) — how to compute
1. Number of faces: triangular prism has 5 faces (2 triangular bases + 3 rectangular lateral faces).
2. Area of each triangular face = (1/2) × base_of_triangle × height_of_triangle = 0.5 · b · h_tri
3. The three rectangular faces each have area = (side_of_triangle) × prism_length
- If triangle sides are a, b, c and prism length (depth) = L:
- Rect face areas = a·L, b·L, c·L
4. Total surface area = 2*(area of triangular base) + (a·L + b·L + c·L)

Example (if helpful)
- Suppose triangular base: base = 6 cm, height = 4 cm → area_tri = 0.5*6*4 = 12 cm²
- Prism length L = 10 cm, triangle side lengths along the perimeter = 6, 5, 7
- Rect areas = 6·10 = 60, 5·10 = 50, 7·10 = 70
- Total SA = 2*12 + (60+50+70) = 24 + 180 = 204 cm²

Send the figure images or the specific dimensions/labels and I’ll compute each blank and identify the exact cross-sections.