**Quadrilateral Limas** – Hi Friends, you must have studied the material for flat shapes and geometric shapes. Well, this article will invite you to study the surface area formulas for rectangular pyramids, pentagonal pyramids, and triangular pyramids, complete with their volumes and types. Come on, read this article to the end!

## What are Limas?

Before discussing the formula for the surface area of a pyramid, it’s a good idea to first understand the meaning of a pyramid. Try to imagine the historic Pyramids in Egypt to make it easier! Yes, it is true. The pyramid shape is basically a rectangular pyramid.

Apart from the pyramids, you can find these spatial shapes in everyday life, from tents, rubik’s rooms, telephone towers, to the top of the temple known as a shikhara or shikhar .

A pyramid is a spatial figure (three dimensions) which has a base in the form of polygons (many terms: triangles, rectangles and pentagons). The sides are triangular and have apex. The name of this shape is determined based on the shape of the base. A cone can be called a pyramid with a circular base, while a pyramid with a square base can be called a pyramid.

A pyramid has n + 1 sides, 2n edges and n + 1 vertices.

## Limas Formula

Now you know the shape of a pyramid shape. Come on, let’s continue the discussion about the pyramid formula. Limas has two kinds of formulas, namely the formula for the surface area and the formula for the volume of a geometric figure. You can use the following formula.

**The formula for the surface area of a pyramid**

The area of the base + the sum of the areas of the perpendiculars (sheath).

**Limas Volume Formula**

⅓ x base area x height

Please note, you need to adjust the formula again to the base area of each shape of the base.

## Types of Limas

Previously, it was mentioned that the name of the type of pyramid is determined by the shape of the base. Therefore, don’t be surprised if the formula for the surface area of a pyramid will be different, depending on the base.

So, what are the types of pyramids? There are triangular pyramids, rectangular pyramids (square), pentagon pyramids, to hexagon pyramids.

## Formulas for Volume and Surface Area of a Pyramid

### 1. Triangular pyramid

A triangular pyramid is a geometric shape that has a triangular base and is conical to one point, so that triangular upright sides are formed.

The characteristics of a triangular pyramid include:

- It has four triangular sides.
- Triangular pedestal.
- Has six ribs, namely AB, AC, BC, AT, BT, and CT.
- It has four vertices, namely A, B, C, and T.

**Volume Formula:**

Volume: ⅓ x (½ xaxt) xt

**Surface Area Formula:**

Surface area: (½ xaxt) + (3 x perpendicular area)

Why is the formula so long? Calm down, the surface area formula inside the brackets is the area of the base. So, all you need to memorize is the area of triangles, squares, pentagons and hexagons.

**Example Question** :

A triangular pyramid T.ABC has a triangular base of 6 cm, a height of 5 cm and a height of 15 cm. Determine the volume of the pyramid!

Discussion:

Is known:

- Triangle base 6 cm.
- Base height 5 cm.
- The height of the pyramid is 15 cm.

Asked: V

Completion:

Those are the definitions, formulas, and examples of triangular pyramid problems. So , do you understand the formula for the volume and surface area of a triangular pyramid?

### 2. Quadrilateral (Square)

A rectangular pyramid is a geometric shape that has a rectangular base, which can be a square, rectangle, rhombus, kite, parallelogram, or trapezoid.

Because the base is rectangular, so it can be known:

- Sum of sides of a triangular pyramid = n + 1 = 4 + 1 = 5 sides.
- Number of triangular pyramid edges = 2 × n = 2 × 4 = 8 edges.
- The number of vertices of a triangular pyramid = = n + 1 = 4 + 1 = 5 vertices.

Following are the properties of a rectangular pyramid:

- Has 5 sides (1 base side and 4 upright sides).
- The sides of the base are rectangular.
- The 4 sides are perpendicular in the shape of a triangle.
- Has 5 corner points.
- Has 8 ribs.

**Volume Formula:**

Volume: ⅓ x (sxs) xt

**Surface Area Formula:**

Surface area: (sxs) + (4 x area of the perpendicular)

### 3. Hexagonal pyramid

**Volume Formula:**

Volume: ⅓ x (2,598 xsxs) xt

**Surface Area Formula:**

Surface area: (2.598 xsxs) + (6 x area of the perpendicular)

If you are still confused about how to get the area of the vertical side, try to pay attention to the triangular shape of the upright side. All you have to do is find the area of the triangle, then multiply the result according to its type (triangle, rectangle, pentagon, or hexagon).

### 4. Five-sided (Pentagonal)

**Volume Formula:**

Volume: ⅓ x (1.72 xsxs) xt

**Surface Area Formula:**

Surface area: (1.72 xsxs) + (5 x area of the perpendicular)

## Example Questions and Discussion

Now, let’s look at an example problem so that you can understand more and get to know more about this one geometric shape. Try again the formula that has been studied together!

**Problem 1**

A rectangular pyramid T.PQRS with a side length of 10 cm has a height of 12 cm. What is the surface area and volume?

**Discussion:**

You can read the problem if the base is rectangular. You can answer this using the surface area formula for a rectangular pyramid.

- Surface area of T.PQRS = area of base + total area of vertical sides (sheath).
- Base area = sxs = 10 x 10 = 100 cm square.
- Total area of perpendiculars = number of triangles x area of triangle QRT or 4 x area of triangle QRT.
- The area of triangle QRT (using Pythagorean calculations), the height of BT is 13 cm.
- Area of triangle QRT = ½ x QR x BT = ½ x 10 x 13 = 65 cm squared.
- The sum of the area of the uprights = 4 x the area of the triangle QRT = 4 x 65 = 260 cm square.

So, the surface area of a rectangular pyramid is = 100 + 260 = 360 square cm.

Next, we find the volume:

- T.PQRS pyramid volume = ⅓ x base area x height.
- So, the volume of T.PQRS is = ⅓ x 100 x 12 = 400 cubic cm.

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That is the meaning, the formula for the surface area of a pyramid, to the example problem. Do you understand about building this space? Hopefully the explanation above can be useful for you and don’t forget to keep practicing so you don’t forget the formulas quickly.