**Related Pages**

Surface Area Formulas

Surface Area of Prisms

Surface Area of a Sphere

More Geometry Lessons

### Surface Area Of A Pyramid

The succeed diagram show how to find the surface area of a pyramid. Scroll down the page for more examples and solutions .

A pyramid is a solid with a polygonal **base** and several trilateral **lateral faces**. The lateral pass faces meet at a common **vertex**. The number of lateral faces depends on the total of sides of the floor. The **height** of the pyramid is the plumb line distance from the base to the vertex .

A regular pyramid has a base that is a unconstipated polygon and a vertex that is above the center of the polygon. A pyramid is named after the shape of its base. A orthogonal pyramid has a rectangle al-qaeda. A trilateral pyramid has a triangle base.

We can find the surface area of any pyramid by adding up the areas of its lateral faces and its base .

Surface area of any pyramid = area of establish + area of each of the lateral faces

If the pyramid is a regular pyramid, we can use the convention for the surface area of a regular pyramid.

Surface sphere of regular pyramid = area of base + 1/2 p

where phosphorus is the circumference of the establish and mho is the pitch acme .

If the pyramid is a square pyramid, we can use the formula for the surface area of a square pyramid .

Surface area of square pyramid = b2 + 2bs

where bel is the length of the base and s is the slant stature .

Worksheets :

Calculate the volume of feather pyramids

Calculate the bulk of prism & pyramids

**Example:**

Calculate the airfoil area of the follow pyramid.

**Solution:**

Sketch a net of the above pyramid to visualize the surfaces.

Since the given pyramid is a square pyramid, we can use any of the above rule .

Using the rule for the surface sphere of any pyramid :

Area of basis = 6 × 6 = 36 cm2

Area of the four triangles = 1/2 × 6 × 12 × 4 = 144 cm2

sum come on sphere = 36 + 144 = 180 cm2

Using the formula for a even pyramid

Surface sphere of regular pyramid = area of base + 1/2 phosphorus

= 6 × 6 + 1/2 × 6 × 4 × 12 = 180 cm2

Using the rule for a square pyramid

Surface area of square pyramid = b2 + 2bs

= 6 × 6 + 2 × 6 × 12 = 180 cm2

### Surface Area Of Pyramid By Adding Up The Area Of Each Surface

How to find the surface sphere of a pyramid by adding up the area of each surface ?

Calculate the surface area of the feather based pyramid.

**Example:**

Find the surface area of a square pyramid with second = 40in, planck’s constant = 39in and newton = 44in

### Surface Area Of Square Pyramid By Using A Formula

How to find the surface area of a square pyramid using the formula ?

Surface area = 2bs + b2 where barn is the distance of the free-base and randomness is the lean altitude .

### Solve Word Problems With Pyramids

**Example:**

What is the come on area of a square pyramid with a free-base area of 255 feather inches and a acme of 7 inches ?

The Great Pyramid of Khufu, the largest of the pyramid in Giza, was built approximately 4,500 years ago. today, the acme of the pyramid is about 455 feet, which is about 30 feet shorter than it was in the first place. If you were to walk wholly around the base of the pyramid, you would have gone about 3,024 feet.

What is the lateral pass coat area of the great pyramid today ?

### Surface Area Of Regular Pyramid By Using A Formula

These videos show how to calculate the surface area of a regular pyramid using the formula :

surface area = sphere of base + 1/2 × circumference of base × cant stature.

S = B + 1/2 phosphorus fifty

### Surface Area Of Pentagonal And Hexagonal Pyramids

This video provides a specific case of how to find the surface area of a pyramid, given al-qaeda edge and height. The base is a pentagon. It shows how to find the apothem and slant height .

#### How To Find The Surface Area Of A Pentagonal Pyramid With The Known Apothem?

### Surface Area Of Regular Pyramid When The Slant Height Is Not Given

How to calculate the open sphere of a hearty pyramid when the slant height is not given ?

Try the free Mathway calculator and problem problem solver below to exercise versatile mathematics topics. Try the given examples, or character in your own trouble and check your answer with the bit-by-bit explanations.

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