Question

Find the lateral area of the right prism with height 0.3 dm, if the base of the prism is Isosceles trapezoid with bases of 3 cm and 5 cm, and legs of 4 cm.

Answer 1

The lateral area of the prism with an isosceles trapezoid base and given dimensions is 0.24 square decimeters.

Step-by-step explanation:

To find the lateral area of a right prism where the base is an isosceles trapezoid, we must calculate the area of each of the trapezoid's non-parallel sides (legs) and then multiply each area by the height of the prism. Since the two legs are equal, we only need to calculate the area for one leg and double it. Let's first convert the given measurement from centimeters to decimeters; 1 cm is equal to 0.1 dm, making the bases 0.3 dm and 0.5 dm, and the legs 0.4 dm. The formula for the lateral area (LA) of a prism is LA = perimeter of base × height. In this case, for the trapezoid, base perimeter does not include the two parallel bases but only the non-parallel sides (legs). The lateral area would be LA = 2 × leg × height = 2 × 0.4 dm × 0.3 dm, which equals 0.24 dm².

Answer 2

The lateral area of that prism consists of 4 rectangles.
h = 0.3 dm = 30 cm.
The lateral area:
A = ( a + b + c + c ) · h
A = ( 5 + 3 + 4 + 4 ) · 30
A = 16 · 30 = 480 cm²
Answer: The lateral area of the prism is 480 cm².