To calculate the total surface area of a prism:.The surface area is made up of the end faces and rectangular faces that join them. ![]() The cross-section of a prism is a polygon, a shape bounded by straight lines. When the cross-section is a hexagon, the prism is called a hexagonal prism.Ī cylinder close cylinder A 3D shape with a constant circular cross-section.When the cross-section is a triangle, the prism is called a triangular prism.cross-section close cross-section The face that results from slicing through a solid shape. can be named by the shape of its polygon close polygon A closed 2D shape bounded by straight lines. Volume is measured in cubed units, such as cm³ and mm³.Ī prism close prism A 3D shape with a constant polygon cross-section. of a prism is the area of its cross-section multiplied by the length. The volume close volume The amount of space a 3D shape takes up. Surface area is measured in square units, such as cm² and mm². shapes and the area of different shapes helps when working out the surface area of a prism. Measured in square units, such as cm² and m². of 3D close surface area (of a 3D shape) The total area of all the faces of a 3D shape. Understanding nets close net A group of joined 2D shapes which fold to form a 3D shape. The number of rectangular faces is the same as the number of edges close Edge The line formed by joining two vertices of a shape. at either end of the prism and a set of rectangles between them. ![]() faces close face One of the flat surfaces of a solid shape. is made up of congruent close congruent Shapes that are the same shape and size, they are identical. The surface area close surface area (of a 3D shape) The total area of all the faces of a 3D shape. The cross-section is a polygon close polygon A closed 2D shape bounded by straight lines. has a constant cross-section close cross-section The face that results from slicing through a solid shape. #GK#, in the middle, is equal to #DC# because #DE# and #CF# are drawn perpendicular to #GK# and #AB# which makes #CDGK # a rectangle.A prism close prism A 3D shape with a constant polygon cross-section. The large base is #HJ# which consists of three segments: ![]() Since we have to find an expression for #V#, the volume of the water in the trough, that would be valid for any depth of water #d#, first we need to find an expression for the large base of trapezoid #CDHJ# in terms of #d# and use it to calculate the area of the trapezoid. The volume of water is calculated by multiplying the area of trapezoid #CDHJ# by the length of the trough. This change affects the length of the large base of the trapezoids at both ends. The water in the trough forms a smaller trapezoidal prism whose length is the same as the length of the trough.īut the trapezoids in the front and the back of the water prism are smaller than those of the trough itself because the depth of the water #d# is smaller than the depth of the trough.Īs the water level varies in the trough, #d# changes. The water level in the trough is shown by blue lines. The volume of prism is calculated by multiplying the area of the trapezoid #ABCD# by the length of the trough.īut we are asked to figure out the volume of the water in the trough, and the trough is not full. The trough itself is a trapezoidal prism. The front and back of the trough are isosceles trapezoids. The figure above shows the trough described in the problem.
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