Read this story to answer the following questions:

Diego is building an architectural rendering of a house. For a portion of the roof, Diego cuts and folds a net for a triangular prism. the base of the prism is an isoceles triangle. the triangle has a base of 24 inches and a height of 5 inches. the distance between the triangular bases is 20 inches.

Based on this story, answer the following answer:

a.)
make an isometric sketch of the folded prism.
b.)
make a sketch of the net of the prism
c.) find the volume of the prism.
D.) find the surface area.

a.) To make an isometric sketch of the folded prism, start by drawing the base triangle. The base triangle should have a length of 24 inches and a height of 5 inches. Next, draw two vertical lines above the base triangle to represent the height of the triangular prism. The distance between these two vertical lines should be 20 inches. Finally, connect the top ends of the vertical lines with the corresponding vertices of the base triangle to complete the sketch.

b.) To create a sketch of the net of the prism, you'll need to unfold the folded prism and lay it out flat. Start by drawing the base triangle with dimensions of 24 inches for the base and 5 inches for the height. Then, draw two identical triangles above and below the base triangle, with 20 inches between their bases and the base triangle. Connect the corresponding vertices of the triangles to create the sides of the net. You should now have a flat, unfolded representation of the prism.

c.) To find the volume of the prism, you can use the formula: volume = base area * height. The base area of an isosceles triangle is given by the formula: base area = (base length * height) / 2. Plugging in the values from the story, we have: base area = (24 inches * 5 inches) / 2 = 60 square inches. The height of the prism is 20 inches. Therefore, the volume of the prism is: volume = 60 square inches * 20 inches = 1200 cubic inches.

d.) To find the surface area of the prism, we need to find the areas of each face and then sum them up. The prism has three rectangular faces and two triangular faces. The area of each rectangular face can be found by multiplying its length by its width. In this case, the length is 24 inches and the width is 20 inches, so each rectangular face has an area of 480 square inches. The area of each triangular face can be found using the formula: area = (base * height) / 2. Using the dimensions from the story, each triangular face has an area of (24 inches * 5 inches) / 2 = 60 square inches. Therefore, the total surface area of the prism is: surface area = (3 rectangular faces * 480 square inches) + (2 triangular faces * 60 square inches) = 1440 square inches + 120 square inches = 1560 square inches.