Example Question - lateral face area
Here are examples of questions we've helped users solve.
Calculating Areas of Base and Lateral Faces of Right Triangular Pyramid
The image shows a right triangular pyramid with a square base. The sides of the square base are 4.5 inches, and the slant height (the height of each triangular face, not the height from the base to the apex) is 4.4 inches. Part A of the question asks for the area of the base and the area of each lateral face. To find the area of the base (A_base), we use the formula for the area of a square: \[ A_{\text{base}} = s^2 \] where \( s \) is the length of a side of the square. Since the side length is 4.5 inches, we calculate the area as: \[ A_{\text{base}} = (4.5\ \text{in})^2 = 20.25\ \text{in}^2 \] To find the area of each lateral face (A_face), we use the formula for the area of a triangle: \[ A_{\text{face}} = \frac{1}{2} \times \text{base} \times \text{height} \] For the lateral faces, the base is the side of the square (4.5 inches), and the height is the slant height (4.4 inches). The area of each lateral face is: \[ A_{\text{face}} = \frac{1}{2} \times 4.5\ \text{in} \times 4.4\ \text{in} = 9.9\ \text{in}^2 \] So, the area of the base is 20.25 square inches, and the area of each lateral face is 9.9 square inches.
Calculating Area of Square Pyramid and Lateral Faces
The image shows a square pyramid with a slant height of 4.4 inches and a base edge length of 4.5 inches. We are asked to solve for the area of the base and the area of each lateral face. Part A: What is the area of the base? Since the base of the pyramid is a square, the area A of a square is given by the formula \( A = s^2 \) where s is the length of a side. Given that s = 4.5 inches, the area of the base is: \[ A = 4.5^2 = 20.25 \] \[ A = 20.25 \text{ square inches} \] The area of the base is therefore 20.25 square inches. Part A also asks for the area of each lateral face. Each lateral face is a triangle with a base of 4.5 inches and a slant height of 4.4 inches which acts as the altitude in this situation. The area A of a triangle is given by the formula \( A = \frac{1}{2}bh \) where b is the base and h is the height (altitude) of the triangle. Using the provided measurements, the area of one triangular lateral face is: \[ A = \frac{1}{2} \times 4.5 \times 4.4 \] \[ A = \frac{1}{2} \times 19.8 \] \[ A = 9.9 \] \[ A = 9.9 \text{ square inches} \] Thus, the area of each lateral face is 9.9 square inches.
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.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com