Example Question - triangular pyramid
Here are examples of questions we've helped users solve.
Calculating Areas of Triangular Pyramid
The image shows a triangular pyramid, and the task is to find the area of the base and the area of each lateral face. The base of the pyramid is a square, with each side measuring 4.5 inches. The area of a square is calculated by squaring the length of one of its sides. Area of the base (A_base) = side_length^2 A_base = (4.5 in)^2 A_base = 20.25 in^2 For the lateral face (each triangular side of the pyramid), the formula for the area of a triangle is used, which is: Area of a triangle (A_triangle) = (base * height) / 2 From the image, it appears that the calculation for one of the triangular faces has already been made: A_triangle = (4.5 in * 4.4 in) / 2 A_triangle = (19.8 in^2) / 2 A_triangle = 9.9 in^2 Therefore, the area of the base of the pyramid is 20.25 square inches, and the area of each lateral face is 9.9 square inches.
Calculating Volume of Triangular Pyramid
The volume \( V \) of a pyramid can be calculated using the formula: \[ V = \frac{1}{3} B h \] where \( B \) is the area of the base and \( h \) is the height of the pyramid. Here, the base is a triangle with a base of 6 inches and a height of 4 inches. First, calculate the area of the triangular base \( A \): \[ A = \frac{1}{2} base \times height = \frac{1}{2} \times 6 \times 4 \] \[ A = 3 \times 4 \] \[ A = 12 \, \text{in}^2 \] Next, use the triangular base area and the height of the pyramid (7 inches) to find the volume: \[ V = \frac{1}{3} \times 12 \times 7 \] \[ V = 4 \times 7 \] \[ V = 28 \, \text{cubic inches} \] So, the volume of the triangular pyramid is 28 cubic inches.
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