Two right triangular prisms are pushed together as shown. The base of one triangle is 12 cm long and 2 cm deep. The height of the triangle is 5 cm.
Determine the exposed surface area of the object when the two triangles are pushed together
The exposed surface area of the object when the two triangles are pushed together includes the two triangle bases as well as the three rectangular sides that are exposed.
First, calculate the surface area of one right triangular prism:
Surface area = base area + lateral area
Base area = (1/2) * base length * height = (1/2) * 12 cm * 5 cm = 30 cm^2
Lateral area = base perimeter * height = 2 * (12 cm + 5 cm) * 5 cm = 170 cm^2
Total surface area of one prism = 30 cm^2 + 170 cm^2 = 200 cm^2
Since there are two prisms pushed together, the total exposed surface area is:
Total surface area = 2 * total surface area of one prism
Total surface area = 2 * 200 cm^2 = 400 cm^2
Therefore, the exposed surface area of the object when the two triangles are pushed together is 400 cm^2.