Question

Знайдіть повну поверхню прямої призми, основою якої є ромб із діагоналями 12 і 16, якщо висота призми дорівнює 10см.

Answer 1

Площа основи призми:
$S_{oc}= \frac{1}{2}*12*16=96$ см².
Площа бічних поверхонь:
$S_{n}=P*h=(2*12+2*16)*10=56*10=560$ см².
Повна поверхня прямої призми:
$S_{nn}=2*S_{oc}+S_{n}=2*96+560=192+560=752$ см².

Answer 2

Finding the Full Surface Area of a Prism with a Rhombus Base

To find the full surface area of a prism with a rhombus base, we can use the formula:

Surface Area = 2 * (area of the base) + (perimeter of the base) * (height)

First, let's calculate the area and perimeter of the rhombus base.

Area of the Rhombus Base

The area of a rhombus can be calculated using the formula: Area = (diagonal1 * diagonal2) / 2

Given that the diagonals of the rhombus are 12 and 16, we can calculate the area: Area = (12 * 16) / 2 = 96 square units

Perimeter of the Rhombus Base

The perimeter of a rhombus can be calculated using the formula: Perimeter = 4 * side

To find the side length, we can use the formula for the side of a rhombus: side = sqrt((diagonal1/2)^2 + (diagonal2/2)^2)

Substituting the given values: side = sqrt((12/2)^2 + (16/2)^2) = sqrt(36 + 64) = sqrt(100) = 10 units

Now, we can calculate the perimeter: Perimeter = 4 * 10 = 40 units

Full Surface Area of the Prism

Now that we have the area and perimeter of the rhombus base, and the height of the prism (10 cm), we can calculate the full surface area using the formula: Surface Area = 2 * 96 + 40 * 10 = 192 + 400 = 592 square units

Therefore, the full surface area of the prism is 592 square units.