Page 2
The perpendicular section of an inclined 4-angled prism is a rhombus with a side of 3 cm. Calculate the area of the lateral surface of the prism if the lateral edge is 12 cm.
Find the lateral surface of an inclined parallelepiped with a side edge of 32 cm and adjacent perpendicular sides of 10 cm and 8 cm.
The side of the base of a regular quadrangular prism is 3 cm. The height of the prism is 5 cm. Find: the diagonal of the base; diagonal of the side face; prism diagonal; base area; diagonal cross-sectional area; lateral surface area; surface area of the prism.
The lateral surface area of a regular quadrangular prism is -32 cm and the surface area is 40 cm. Find the height of the prism.
Solution. The area of the base is S = (cm2), the side of the base is 2 cm, the perimeter of the base is P = 8 cm, and the height of the prism 
(cm2).
Triangular, hexagonal and n-gonal prisms.
Before solving problems, it is advisable to repeat the formulas; Sb = RN and Sp = 2Sb + 2s for an arbitrary prism, as well as the formulas:
Р = 3а, s = - for regular triangular and
P = 6a, s = - for a regular hexagonal prism with base side a.
The distances between the side edges of an inclined triangular prism are: 2 cm, 3 cm and 4 cm. The lateral surface of the prism is 45 cm." Find its side edge.
Solution. In the perpendicular section of the prism there is a triangle (Fig. 4.3), the perimeter of which is 2 + 3 + 4 = 9 (cm), so the side edge is equal to 45: 9 = 5 (cm).
Calculate the lateral surface area of a regular triangular prism if it is known that the cross-sectional area passing through the center lines of the bases is 25 cm."
Solution. In cross-section it is a rectangle, one side of which is equal to the side edge, and the other is half the side of the base (Fig. 4.4). Consequently, its area is 2 times less than the area of the side face. So, the area of the side face is 50 cm", and the side surface is 50 ∙ 3 = 150 (cm").
Each edge of a regular triangular prism is 12 cm. Calculate: the area of the base; lateral surface area; surface area; the area of the section drawn through the median of the base and a lateral edge that passes through one vertex of the base.
In a right triangular prism, all edges are equal. The lateral surface area is 12 cm." Find the height.
Find the unknown elements of a regular triangular prism using the elements given in Table 3.
Option 1.
Exercise 1. Draw a triangular pyramid. Define a pyramid. What is the height of a pyramid? The basis? Side edge? Which pyramid is called correct? What is an apothem? How to calculate the lateral surface area of a pyramid? How to calculate the total surface area of a pyramid?
Task 2 . Answer the questions:
Is it true that all the faces of a right prism are rectangles?
Is a prism a polyhedron or a polygon?
What is the basis of a regular triangular prism?
What can you say about the side ribs of the prism?
When is the height of a prism equal to its side edge?
Is it true that if two lateral faces of a prism are perpendicular to the plane of the base, then the prism is straight?
What geometric figures are the lateral faces of a straight prism?
How many diagonals does a quadrangular prism have?
Can a cross section of a cube divide it into two regular prisms?
Is a tetrahedron a type of prism or pyramid?
What elements of a regular 4-gonal prism need to be known in order to calculate the area of its lateral surface?
ABCDA 1 IN 1 WITH 1 D 1 Dwith sides AB and CD.
How many degrees is the angle between the side edge and the base of the straight prism?
In a triangular pyramidDDAB andD
CubedABCDA 1 IN 1 WITH 1 D 1 a section parallel to ribs AB and CC is drawn 1
Is it true that if a prism is regular, then all the edges of its base are equal?
INpyramidDABC ribsDA,DIn andDC are equal. Determine the type of triangle ABC if the base of the altitude of the pyramid lies outside triangle ABC.
DABC, parallel to the ribsDA and BC. Determine the type of polygon obtained in section.
Test on the topic "Polyhedra"
Option 2.
Exercise 1 . Draw a triangular prism. Define a prism. What is the height of a prism? The basis? Side edge? Which prism is called a straight prism? Which prism is called correct? How to calculate lateral surface area
prisms? How to calculate the total surface area of a prism?
Task 2 . Answer the questions:
Is it true that all faces of an inclined prism are parallelograms?
Is a cube a type of prism or pyramid?
What will the prism be like if its side edges are perpendicular to the bases?
Is a pyramid a polyhedron or a polygon?
What lies at the base of a regular quadrangular prism?
What geometric shapes are the lateral faces of the pyramid?
How many diagonals does a triangular prism have?
Is it true that if two adjacent lateral faces of a prism are perpendicular to the plane of the base, then the prism is straight?
What can you say about the bases of the prism?
Is it possible to find the lateral surface area of a regular pentagonal prism, knowing only the side of its base and its height?
When is the lateral edge of a prism greater than its height?
Can a cross section of a cube divide it into two right triangular prisms?
Name two pairs of parallel faces of a right prismABCDA 1 IN 1 WITH 1 D 1 if its base is trapezoid ABCDwith sides ADand VS.
In a triangular pyramidDABC name the height if the side edgesDAC andDBC are perpendicular to the base of ABC.
CubedABCDA 1 IN 1 WITH 1 D 1 a section parallel to ribs BC and AA was drawn 1 . Determine the type of polygon obtained in section.
Is it true that if all the edges of the base of a right prism are equal, then it is regular?
INpyramidDABC ribsDA,DIn andDC are equal. Determine the type of triangle ABC if the base of the height of the pyramid lies on segment AC.
Plane intersecting a regular tetrahedronDABC, parallel to ribs CDand AB. Determine the type of polygon obtained in section.