Let’s solve this step by step.
We are given a 3D shape — it looks like two pyramids stuck together at their bases (a bipyramid). The shaded part is one of the triangular faces on the bottom pyramid. We need to find the area of that shaded triangle.
Looking at the diagram:
- The base of the shaded triangle is labeled
14 in.
- There’s a dashed line inside the shaded triangle, perpendicular to the 14-inch side, labeled
12 in. That’s the height of the triangle!
- The little square symbol means it’s a right angle → so yes, 12 inches is the height corresponding to the 14-inch base.
So, we have a triangle with:
- Base = 14 inches
- Height = 12 inches
Area of a triangle = (base × height) ÷ 2
Let’s calculate:
14 × 12 = 168
168 ÷ 2 = 84
So the area is 84 square inches.
Wait — let me double-check. Is the 12-inch line really the height of the shaded triangle? Yes — because it’s drawn from the opposite vertex straight down to the 14-inch side, and there’s a right-angle mark. So it’s definitely the height for that base.
Also, the 13-inch line is probably the height of the top pyramid — but we don’t need that for the shaded triangle’s area. It might be a distractor.
Final check: Triangle area formula is correct. Multiplication and division are correct.
✔ Answer is 84.
Final Answer:
84
Parent Tip: Review the logic above to help your child master the concept of volume of triangular pyramids worksheet.
