The total amount of space taken up by an object is called the surface area.It is the total area of all the surfaces of that object.It is easy to find the surface area of a three-dimensional shape if you know the correct formula.You need to identify the shape you're working with in order to work with it.It is possible to remember the surface area formula for various objects in the future.Here are some of the most common shapes.
Step 1: Define the formula for the cube's surface.
There are six square sides to the cube.The area of a square is determined by the length of the side and the width.To find the surface area of a cube, simply divide the area by 6.The length of one side is the formula for the surface area of a cube.The units of surface area will be in, cm, m, etc.
Step 2: Take the length of one side.
You only need to measure one side of a cube if it's equal in length to the others.Measure the length of the side with a ruler.Look at the units you are using.The measurement should be marked down as a.A is 2 cm.
Step 3: For your measurement, square it.
The measurement is taken for the length of the edge.To square a measurement is to add it up.It's a good idea to write it as SA when you're first learning these formulas.This step shows the area of one side of the cube.2 x 2 is equal to 4 cm.
Step 4: Divide this product by six.
The cube has six sides.To account for all six sides, you need to divide the area by six.The cube's surface area is calculated using this step.A Surface Area of 6 x 4 is 24 cm.
Step 5: The formula for the surface is rectangular.
Unlike a cube, the sides of a rectangular prism are not exactly the same.The opposite sides are equal.The side lengths of the formula SA are taken into account when calculating the surface of a rectangular prism.The width, height, and length are all equal for this formula.Adding up the areas of each face of the object is what you can see in the formula.The units of surface area will be squared off.
Step 6: Measure the length, height, and width of each side.
All three measures need to be taken separately.Measure each side and write it down.The same units are used for each measurement.Measure the base's length to determine the length of the prism, and then assign this to a.If you measure the side's height, you can assign it to b.b is 3 cm.
Step 7: Take the area of one of the sides and divide by two.
There are 6 faces of a rectangular prism, but the opposite sides are the same.To find the area of one face, divide the length and height by c and a.To account for the opposite identical side, take this measurement and divide it by two.2 x 5 x 10 is 20 cm.
Step 8: You can find the area on the other side of the prism.
The width and height of the first pair of faces can be used to find the area of another face.To account for the opposite identical sides, divide this measurement by two.2 x (a x b)2 x (2 x 3)6 x 12 cm
Step 9: Take the area of the ends and divide it by two.
The ends will be the final faces of the prism.To find their area, divide the length and width by c and b.To account for both sides, divide this measurement by two.2 x (b x c) is the same as 3 x (3 x 5) and is 30 cm.
Step 10: Add the three measurements together.
The final step is to add all of the calculated areas together.To find the total surface area, add the area measurement for all the sides together.The surface area is divided by the number of 30 and 20
Step 11: Define the surface area formula.
There are two triangular sides and three rectangular faces.To find the surface area, you have to add all of the sides together.The area of the triangular base is A, the perimeter is P and the height is h.B is the base of the triangle and h is its height.Adding all three sides of the triangle together is how P is calculated.The units of surface area will be squared off.
Step 12: Take the area of the face and divide it by two.
The area of a triangle is 2b*h, where b is the base and h the height.We can divide the formula by two because there are two identical triangle faces.The base, b, is the length of the triangle.The height of the triangular base is the distance between the bottom edge and the top peak.h is the Area of the one triangle divided by 2.
Step 13: Measure each side of the triangle.
To calculate the surface area, you need to know the length of each side of the triangle.The height is the distance between the two faces.The three sides are referred to as the triangular base.S1 is 2 cm and S2 is 4 cm.
Step 14: The perimeter of the triangle should be determined.
Adding up the sides of the triangle can be used to calculate the perimeter.P, S1, S2, S3 and S4 are all equal to 12 cm.
Step 15: The perimeter of the base can be calculated by height.
There is a distance between the two bases.P x H is 12 x 5 x 60 cm.
Step 16: Add the two measurements together.
To calculate the triangular prism's surface area, you will need to add the two previous steps together.The example is 72 cm.
Step 17: Define the formula for the sphere.
The mathematical constant pi is used to calculate the surface area of a sphere.The surface area of a sphere is given by an equation.It should be approximated to 3.14.The units of surface area will be in, cm, m, etc.
Step 18: Measure the distance from one point to another.
Half the diameter of the sphere is half the distance from one side to the other.R is 3 cm.
Step 19: The circle is the radius.
You can square a number by itself.Take the measurement and divide it by itself.The formula can be changed as SA is 4r*r.
Step 20: If you use an approximation of pi, you'll get the squared radius.
The ratio of a circle's circumference to its diameter is represented by Pi.It is an irrational number.It is usually approximated as 3.14.To find the area of one circular section of the sphere, you have to use the squared radius.*r is 3.14 x 9 x 28.26 cm.
Step 21: Divide this product by four.
If you want to complete the calculation, multiply by 4.Take the flat circular area and divide it by four to find the surface area of the sphere.The 4*r is 4 x 28.26
Step 22: Define the formula for the cylinder.
A cylinder has two ends.The formula for surface area of a cylinder is SA, where r and h are the radius and height of the cylinder.Round pi to 3.14.The surface area of the two circular ends and the column connecting them are represented by 2*r.The units of surface area will be squared off.
Step 23: The cylinder's height and radius should be measured.
Half the diameter of the circle is half the distance from one side to the other.The total distance from end to end is the height.Take the measurements and write them down with a ruler.R is 3 cm and h is 5 cm.
Step 24: Take the area of the base and divide it by two.
The formula for the area of the base is *r.The second identical circle on the other end of the cylinder is taken into account.2*r is the area of base which is 2 x 28.26 cm.
Step 25: The cylinder's surface area can be calculated using 2*rh.
This formula is used to calculate the surface area of a tube.There is a tube between the two ends of the cylinder.If you add the height and pi, you get the radius.2 x 3.14 x 3 x 5 is 94.2 cm.
Step 26: Add the two measurements together.
To calculate the total surface area of the cylinder, add the surface areas of both circles to the space between them.Adding the two pieces together will allow you to recognize the original formula.2*r + 2h + 94.2 + 150.72 cm is an example.
Step 27: The square pyramid has a surface area formula.
There is a square base and four triangular sides.The area of square is the length of one side.The area of a triangle is divided into 1/2sl by the length or height of the triangle.To find the total surface area, you have to divide it by four.The equation of surface area for a square pyramid is SA + 2sl.The length of each side of the square base is referred to as s and the slant height as l.The units of surface area will be in, cm, m, etc.
Step 28: Take a look at the slant height and base side.
The slant height is the height of one of the triangular sides.It is the distance from the base to the peak of the pyramid.The length of the square base is s.This measurement is the same for all sides because the base is square.To make each measurement, use a ruler.l is 3 cm and s is 1 cm.
Step 29: The square base has an area.
The area of a square base can be calculated by taking the length of one side and dividing it by itself.1 x 1 is 1 cm.
Step 30: The four triangular faces have a total area.
The fourth triangular side's surface area is the second part of the equation.The formula 2ls can be used to calculate s by l and two.You can find the area of each side by doing that.2 x s x l x 1 x 3 is 6 cm
Step 31: The two separate areas should be combined.
To calculate the total surface area, add the sides to the base.S + 2sl + 1 + 6 is 7 cm.
Step 32: Define the formula for a cone.
A cone has a circular base and a rounded surface.To find the surface area, you need to calculate the area of the circular base and the cone together.The formula for the surface area of a cone is: SA + *rl, where r is the angle of the cone, l is its slant height, and the mathematical constant pi (3.14).The units of surface area will be in, cm, m, etc.
Step 33: The cone's height and radius are measured.
The side of the base is closer to the center of it's circular base.The height is the distance from the base to the top of the cone.r is 2 cm and h is 4 cm.
Step 34: The cone's slant height is calculated.
The Pythagorean Theorem is used to calculate the slant height.The rearranged form is (r + h), where the radius is and the height is.The figure is (2 x 2 + 4 x 4) and it's 4.27 cm.
Step 35: Determine the location of the base.
The area of the base is calculated using the formula *r.*r is the amount of 2 x 2 divided by 12.56 cm.
Step 36: The cone's surface area is calculated.
You can find the top part of the cone using the formula *rl, where r is the circle's radius and l is its slant height.The figure is 3.14 x 2 x 4.47 cm.
Step 37: To find the total surface area, add two areas together.
Add the area of the circular base to the calculation to calculate the final surface area.The example is 40.63 cm.