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What is the missing length l of the triangular prism of the surface area is 524 square centimeter

10cm
10cm
6cm
8cm

2 answers

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.
The real answer is 17cm. (For POA students in 7th grade "Surface Area of Triangular Prisms" Lesson's Quick check!!) Trust me!!