What is the missing length l of the triangular prism of the surface area is 524 square centimeter
10cm
10cm
6cm
8cm
The real answer is 17cm. (For POA students in 7th grade "Surface Area of Triangular Prisms" Lesson's Quick check!!) Trust me!!
To find the missing length l of the triangular prism, we need to use the formula for the surface area of a triangular prism, which is:
Surface Area = 2*(base area) + (perimeter of base)*height
Given:
Base dimensions: 10cm, 10cm, 6cm
Height: l
Surface Area: 524 cm^2
First, find the base area:
Base Area = (1/2)*(base1)*(base2)
Base Area = (1/2)*(10cm)*(6cm)
Base Area = 30 cm^2
Next, find the perimeter of the base:
Perimeter of base = 10cm + 10cm + 6cm
Perimeter of base = 26 cm
Now, plug the values into the formula for the surface area:
524 cm^2 = 2*30 cm^2 + 26 cm * l
524 cm^2 = 60 cm^2 + 26 cm * l
Subtract 60 cm^2 from both sides:
464 cm^2 = 26 cm * l
Divide by 26 cm:
l = 464 cm^2 / 26 cm
l = 17.846 cm
Therefore, the missing length l of the triangular prism is approximately 17.85 cm.