Question

Бічне ребро прямої чотирикутної призми дорівнює 5 см. Знайдіть площу бічної поверхні призми, якщо її осно- ва — прямокутник, діагональ якого дорівнює 10 см, а одна зі сторін — 8 см.

Answer 1

$S_{b}=P_{osnovu} * h$
Щоб знайти периметр розглянемо прямокутник. Діагональ ділить його на 2 прям. трикутники і слугує для них гіпотенузою: 10см. Нам дано один з катетів: 8 см.
знайдемо інший за теор. Піфагора:
2-й кат.=$\sqrt{10^{2}-8^{2}}=\sqrt{100-64}=\sqrt{36}=6$ (см)
P=2(a+b)=2*(8+6) = 2*14= 28
Sбіч= 28*5=140(см^2) 

Answer 2

Finding the lateral surface area of a rectangular prism

To find the lateral surface area of a rectangular prism, we need to know the length of the lateral edge and the dimensions of the base.

Given: - The length of the lateral edge of the prism is 5 cm. - The base of the prism is a rectangle with a diagonal of 10 cm and one side measuring 8 cm.

To find the lateral surface area, we need to calculate the perimeter of the base and multiply it by the length of the lateral edge.

Let's calculate the perimeter of the base first. Since we know the diagonal and one side of the rectangle, we can use the Pythagorean theorem to find the other side.

Using the Pythagorean theorem: - Diagonal = 10 cm - One side = 8 cm

Let the other side be 'x' cm.

According to the Pythagorean theorem, the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.

So, we have: 8^2 + x^2 = 10^2

Simplifying the equation: 64 + x^2 = 100 x^2 = 100 - 64 x^2 = 36 x = √36 x = 6 cm

Now we know the dimensions of the base: - One side = 8 cm - Other side = 6 cm

The perimeter of the base is the sum of all sides: Perimeter = 2 * (8 + 6) = 2 * 14 = 28 cm

Now, we can calculate the lateral surface area by multiplying the perimeter of the base by the length of the lateral edge: Lateral Surface Area = Perimeter * Length of Lateral Edge Lateral Surface Area = 28 cm * 5 cm = 140 cm^2

Therefore, the lateral surface area of the given rectangular prism is 140 cm^2.