Find the lateral and surface area of the right rectangular prism whose length is 7 cm, width is 5 cm, and height is 1.5 cm. I got 36 as my lateral area and 106 as my surface area. Is this right?
To find the lateral area of a right rectangular prism, you need to add the areas of all the four sides of the prism. In this case, the lateral area is the sum of the areas of the four sides of the prism.
The formula to find the lateral area of a right rectangular prism is:
Lateral Area = 2 × (length × height) + 2 × (width × height)
Let's substitute the given values into the formula:
Length = 7 cm
Width = 5 cm
Height = 1.5 cm
Lateral Area = 2 × (7 cm × 1.5 cm) + 2 × (5 cm × 1.5 cm)
Lateral Area = 2 × (10.5 cm^2) + 2 × (7.5 cm^2)
Lateral Area = 21 cm^2 + 15 cm^2
Lateral Area = 36 cm^2
So, your calculation for the lateral area of 36 cm^2 is correct.
To find the surface area of a right rectangular prism, you need to add the areas of all the six faces of the prism. In this case, the surface area is the sum of the areas of the six faces of the prism.
The formula to find the surface area of a right rectangular prism is:
Surface Area = 2 × (length × width) + 2 × (length × height) + 2 × (width × height)
Let's substitute the given values into the formula:
Length = 7 cm
Width = 5 cm
Height = 1.5 cm
Surface Area = 2 × (7 cm × 5 cm) + 2 × (7 cm × 1.5 cm) + 2 × (5 cm × 1.5 cm)
Surface Area = 2 × (35 cm^2) + 2 × (10.5 cm^2) + 2 × (7.5 cm^2)
Surface Area = 70 cm^2 + 21 cm^2 + 15 cm^2
Surface Area = 106 cm^2
So, your calculation for the surface area of 106 cm^2 is correct.
Therefore, both your calculations for the lateral area and surface area are correct.