finding the volume of a trapezoidal prism

#Finding the volume of a trapezoidal prism plus

The diagram at the right should clarify this further,Īs well as give a physical basis for this relationship. Now is a good time to review something learned in algebra, namely Understanding surface area may be clearer if you refer back to the netĪt left is a net for a cube and at right a portion of a net for a sphere.Įach of these portions of a sphere is called a gore. The lateral surfaces are all triangles with a base of 20'Īnd a height (the slant height) of 26'. The height is one leg and 20'/2 = 10' is the other leg. The slant height is the hypotenuse of a right triangle where The surface area of a sphere is equal to 4 r 2.Īnalogous to the unit circle is the unit sphere.Įxample: Consider a right pyramid A-BCDE with vertex AĪnswer: We don't need the height for this calculation,īut we will calculate it anyway to stress the difference between slant heightĪnd height.

#Finding the volume of a trapezoidal prism plus

The surface area of a pyramid or cone is the lateral area plus the N = 2 for prisms/cylinders n = 1 for pyramids/cones n = 0 for spheres. Since the bases for a prism or cylinder areĬongruent, this is often expressed as twice the area of the base. The surface area of a prism or cylinder is the lateral area plus theĪrea of each base. The surface area of a figure is the sum of the area of all surfaces of a figure. It depends on if you can obtain the altitude (slant height) of each triangular face.

(which is a fancy way to say you may need calculus). The surface area might not be calculatable using elementary techniques If the pyramid is irregular and certainly if the cone is oblique, Of the base where it is halfway between the base's vertices. The slant height is the distance from the vertex to the edge The lateral area is thus half the slant height times the perimeter. Prisms, but since each face is a triangle (or triangle-like),

The lateral area of a regular pyramid or right cone is similar to that of Lateral Area of a right cone: ½ perimeter × slant height. Lateral Area of a regular pyramid: ½ perimeter × slant height. Lateral Area of a cylinder: circumference × height. Lateral Area of a prism: perimeter × height Multiply this length by the width, which was the height of the can. To find the area of this rectangle which is the same as the lateral area, What was the circumference of the base is now the length of a rectangle.

Now cut down the side of the can and roll it flat. The lateral area is the surface area of a 3D figure, Volume: prism/cylinder, pyramid/cone, sphere.Surface Area: prism/cylinder, pyramid/cone, sphere.Lateral Area: prism/cylinder, pyramid/cone.Surface Area and Volume Back to the Table of Contents A Review of Basic Geometry - Lesson 10 Lateral & Surface Areas, Volumes Lesson Overview