find area of base of a cube is
Answers
Answer:
Step-by-step explanation:
Square Bases
Cubes and square pyramids have bases that are square-shaped. The area of a square is equal to the length of one of its sides multiplied by itself, or squared. The formula is A = s2. For example, to find the area of a base of a cube with 5-inch sides: A = 5 inches x 5 inches = 25 square inches
Rectangular Bases
Some rectangular solids and pyramids have rectangular bases. The area of a rectangle is equal to its length, l, multiplied by its width, w: A = l x w. Given a pyramid whose base is 10 inches long and 15 inches wide, find area as follows: A = 10 inches x 15 inches = 150 square inches.
Circular Bases
The bases of cylinders and cones are circular. The area of a circle is equal to the circle's radius, r, squared then multiplied by a constant called pi: A = pi x r2. Pi always has the same value, approximately 3.14. While pi technically has an endless number of decimal places, 3.14 is a good enough estimation for simple calculations. For example, given a cylinder with a radius of 2 inches, you can find the base's area as follows: A = 3.14 x 2 inches x 2 inches = 12.56 square inches.
Triangular Bases
A triangular prism has a triangular base. Finding a triangle's area requires two known quantities: base, labeled b, and height, labeled h. Base is the length of one of the triangle's sides, height is the distance from that side to the opposite corner of the triangle. The area of the triangle is equal to half of the base times the height: A = b x h x 1/2 You could find the area of a triangle with base length of 4 inches and height of 3 inches as follows: A = 4 inches x 3 inches x 1/2 = 6 square inches.
Lateral Area of a Cube
A cube has six faces of equal area, and 12 edges of equal length. A cube's two bases -- its top and bottom -- are both squares, and are parallel to each other. You can find the lateral area of a solid with parallel bases by multiplying the perimeter of the base -- the length around the edge of the base -- by the solid's height. The perimeter of a cube's base is equal to four times the length of one of the cube's edges, s. The height of the cube is also equal to s. So lateral area, LA, is equal to 4s multiplied by s:
LA = 4s^2
Take a cube with edges 3 inches long. To find its lateral area, multiply 4 times 3 times 3:
LA = 4 x 3 inches x 3 inches LA = 36 square inches
Lateral Area of a Cylinder
A cylinder's lateral area is the area of the rectangle that wraps around the cylinder's side. This is equal to the height of the cylinder, h, times the perimeter of one of its circular bases. The perimeter of the base is equal to the radius of the cylinder, r, multiplied by 2 times pi. So a cylinder's lateral area uses the following formula:
LA = 2 x pi x r x h
Take a cylinder with radius of 4 inches and height of 5 inches. You can find lateral area as follows. Note that pi is approximately 3.14.
LA = 2 x 3.14 x 4 inches x 5 inches LA = 125.6 square inches
Lateral Area of a Prism
A prism's lateral area is equal to one of its bases' perimeter times its height:
LA = p x h
Take a triangular prism 10 inches high, whose triangular bases have side lengths of 3, 4, and 5 inches. The perimeter is equal to the sum of the side lengths: 12 inches. So to find lateral area, you'd multiply 12 by 10:
LA = 12 inches x 10 inches LA = 120 square inches
Lateral Area of a Square Pyramid
A pyramid only has one base, so you cannot use the base perimeter times height formula. Instead, a pyramid's lateral area is equal to one-half the perimeter of its base times the pyramid's slant height, s:
LA = 1/2 x p x s
For example, take a square pyramid whose base has sides of 7 inches long, and with a slant height of 14 inches. Since the base is a square, its perimeter will be 4 times 7, 28:
LA = 1/2 x 28 inches x 14 inches LA = 196 square inches
Lateral Area of a Cone
The formula for a cone's lateral area is the same as that of the pyramid: LA = 1/2 x p x s where s is the slant height. However, since a cone's base is a circle, you solve for its perimeter using the cone's radius:
p = 2 x pi x r LA = pi x r x s
Given a cone with radius of 1 inch and slant height of 8 inches, you can use this formula to solve for lateral area:
LA = 3.14 x 1 inch x 8 inches LA = 25.12 square inches
Radius and Pi
The radius, usually noted as "r," of a cone is the distance from the center of the cone's base to the side of the cone's base. Pi is defined as the circumference of a circle divided by its diameter. It always has the same value: roughly 3.14. Depending on the level of precision you need in your calculations, pi can be extended to an endless number of digits after the decimal point. For example, pi extended to seven digits would be 3.1415926. However, 3.14 is considered a good enough approximation for basic geometry equations.