Two right triangular prisms are pushed together as
x
shown. The base of one triangle is 12 cm long and 2 cm deep. The height of the triangle is 5 cm.
b. Determine the exposed surface area of the object when the two triangles are pushed together.
First, we need to calculate the surface area of each right triangular prism separately.
For the first prism:
Base area = 1/2 * 12 cm * 2 cm = 12 cm²
Lateral area = 12 cm * 5 cm = 60 cm²
Total surface area of the first prism = Base area + Lateral area = 12 cm² + 60 cm² = 72 cm²
Since the two right triangular prisms are pushed together, the base of the second triangle aligns with the base of the first triangle. Therefore, the exposed lateral area of the object is the sum of the lateral areas of each prism, minus the area of the shared base.
Since the total lateral area of each prism is 60 cm², we have:
Total lateral area of the object = 60 cm² + 60 cm² = 120 cm²
Since the shared base has an area of 12 cm², the exposed surface area of the object when the two triangles are pushed together is:
120 cm² - 12 cm² = 108 cm²
Therefore, the exposed surface area of the object when the two triangles are pushed together is 108 cm².