Question

ПОМОГИТЕ ПРОШУ Известно, что в прямой призме основанием является ромб с диагоналями 3 и 4. Высота призмы равна 3,5. Найди площадь поверхности призмы. Если результатом является дробное число, укажи его в десятичном виде.

Answer 1

Ответ:

Sпп = 47

Объяснение:

дано:  прямая призма

осн. ромб d1=3,  d2=4

h=3.5

Sпп= Sбок + 2Sосн

Sбок=Р*h

Р - периметр, т.к. это ромб то  Р=4а ( а - сторона ромба)

по т.Пифагора    а=√[(d1/2)²+(d2/2)²]=1/2*√(3²+4²)=2.5

P = 4*2.5=10

Sбок=10*3,5=35

Sосн=0,5d1*d2=0,5*3*4=6

Sпп = 35 + 2*6 = 35 + 12 = 47

Sпп = 47

Answer 2

Calculation of the Surface Area of a Prism

To find the surface area of a prism, we need to calculate the areas of all its faces and then sum them up.

In this case, we are given that the base of the prism is a rhombus with diagonals measuring 3 and 4 units. The height of the prism is 3.5 units.

Let's break down the calculation step by step:

1. Calculate the area of the base: - The base of the prism is a rhombus. - The formula to find the area of a rhombus is: Area = (diagonal1 * diagonal2) / 2. - Plugging in the given values, we get: Area = (3 * 4) / 2 = 6.

2. Calculate the areas of the lateral faces: - The lateral faces of the prism are rectangles. - The formula to find the area of a rectangle is: Area = length * width. - The length of the rectangle is equal to the perimeter of the base, which can be calculated by multiplying one side of the rhombus by 4. - The width of the rectangle is equal to the height of the prism. - Plugging in the values, we get: Area = (3 + 3 + 4 + 4) * 3.5 = 49.

3. Calculate the total surface area: - The total surface area of the prism is the sum of the areas of the base and the lateral faces. - Plugging in the values, we get: Total Surface Area = Base Area + Lateral Face Area = 6 + 49 = 55.

Therefore, the surface area of the given prism is 55 square units.

Please let me know if you need any further assistance!