A triangular pyramid with a base length of 9 inches, a base height of 10 inches, and \( 200 \mathrm{~m} / \mathrm{n} \) Required \( 0 / 7 \) height of 32 inches. 10. What is the volume of the figure? Type a response Show Your Work

To find the volume of a triangular pyramid (also known as a tetrahedron), you can use the following formula: \[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \] **Given:** - **Base Length (b)** = 9 inches - **Base Height (h₁)** = 10 inches - **Pyramid Height (H)** = 32 inches **Step 1: Calculate the Base Area** The base of the pyramid is a triangle. The area of a triangle is given by: \[ \text{Base Area} = \frac{1}{2} \times \text{Base Length} \times \text{Base Height} \] Plugging in the values: \[ \text{Base Area} = \frac{1}{2} \times 9\,\text{in} \times 10\,\text{in} = \frac{1}{2} \times 90\,\text{in}^2 = 45\,\text{in}^2 \] **Step 2: Calculate the Volume of the Pyramid** Using the volume formula: \[ \text{Volume} = \frac{1}{3} \times 45\,\text{in}^2 \times 32\,\text{in} = \frac{1}{3} \times 1,440\,\text{in}^3 = 480\,\text{in}^3 \] **Answer:** The volume of the triangular pyramid is **480 cubic inches**.