TITLE: SURFACE AREA OF SOLID / SPACE FIGURES

OVERVIEW:
Surface area is a fundamental concept in geometry that quantifies the total
area of the outer surfaces of a three-dimensional object, known as solid or space
figures. It plays a crucial role in various real-world applications, such as
architecture, engineering, and physics. Understanding surface area is essential for
designing structures, optimizing materials, and solving problems related to heat
transfer and fluid dynamics.
Solving problems related to surface area requires critical thinking and
application of mathematical concepts. Real-world scenarios often involve optimizing
surface area to achieve specific goals, making it a valuable skill in problem-solving.

OBJECTIVES:
 Understand the concept of surface area as the sum of the areas of all
exposed surfaces of a three-dimensional object.
 Recognize and describe common three-dimensional shapes, including
cubes, rectangular prisms, cylinders, spheres, and cones.
 Analyze and calculate the surface area of composite figures composed
of multiple simpler shapes.

DISCUSSION OF CONTENT:

Surface Area (S.A) is the sum of the areas of the base and the lateral faces of a solid figure.
Surface area is measured in square units such as cm², ft², m², and other units. One way to find the
surface area of a solid figure is to find the area of its nets.

A. Surface Area of Prism

A prism is a polyhedron that has two congruent parallel faces called bases. There are
many kinds of prism. A prism is named according to the shape of its base.

 Rectangular prism

There are six surfaces in a rectangular prism. It is composed of two rectangular

bases and four rectangular lateral faces. Rectangular prism has 8 vertices and 12
 edges. The surface are of rectangular prism is the total area of the top, bottom,
front, back, left side and right side of rectangles.
Another way to find the surface area of the rectangular prism is to use the
lateral area and base areas. Lateral (L.A) of a prism is the sum of the areas of
lateral faces. It is important to find the lateral area of prism first. Lateral faces
are the faces in a prism that are not base.
The surface area of rectangular prism is the sum of the lateral area and
the area of the two bases. S.A = 2B + L.A or S.A = 2lw +2lh +2wh

 Triangular Prism

A triangular prism has five faces. These five faces are composed of two
triangular bases and three rectangular lateral faces. It has also 6 vertices and 9
edges. In the triangular prism, the front triangle face is connected to the rear
triangle face by the three rectangle faces. The triangle faces are considered the
bases, and the rectangle faces are considered lateral faces.

In finding the surface area of the triangle prism, find its Lateral Area (L.A) first.
The lateral area of the triangular prism is the product of the perimeter (p) of the
base and height (h). (L.A = ph)

Surface area (S.A) of triangular prism is equal to the sum of its Lateral Area (L.A)
and area of 2 bases. (S.A = L.A + 2B)

 Cube
 A cube is square prism. There are six surfaces of a cube. The bases and the faces
have equal sizes. Cube has 8 edges and 12 edges.
To get the Surface area (S.A) of a cube, the six faces is multiplied to the square
of the length or side (s). (S.A = 6s²)

B. Surface Area of Cylinder

A cylinder has three surfaces: the two bases and one curved surface or lateral surface. It
has no vertex and edge. The bases form circles. The curved or lateral surface forms
rectangle. The height ( or width) of the rectangle is the height of the cylinder. The base
length of the rectangle is the circumference of the cylinder.

L.A = 2πrh Area of a Base (B) = πr² S.A = L.A +2B

The lateral area of a cylinder is the product of the circumference of the base and the
height of the cylinder. (L.A = 2πrh)

C. Area of a Cone
 A cone has one circular base and a curved surface with apex or vertex. It has no edge.
The area of the circular base and the area of the curved surface determine the surface
area of a cone.

The surface area of a cone is the sum of the lateral area (L.A) and the area of its
base (B). (S.A = L.A +B)
To find the lateral area (L.A), imagine cutting the lateral surface into wedges and
arranging the wedges to form a figure like a parallelogram.
The base of the new figure is πr and the height is the slant height of the curved
surface. So, L.A = πrs. Thus, the surface area of cone is S.A = L.A + B or S.A = πrs + πr².

D. Surface Area of Sphere

A sphere is perfectly round and symmetrical solid figure. It has no edges and vertices. It
is curved surface of points that are all of the same distance from the center. Like a circle,
the distance from the center of a sphere to the surface is known as the radius (r).

The area of the circle that contains the center of the sphere is πr² it would take
exactly 4 of these circles too wrap the sphere completely. The surface area of a sphere
with radius ® is S.A = 4πr².
 E. Pyramid

Pyramids are named according to the shape of its base. Examples of pyramids include
square pyramid, rectangular pyramid and triangular pyramid. The surface area of any
pyramid is the sum of the areas of all the faces, including the base. We can use the net
to find a general formula that will help us find the surface area of any pyramid.

The surface area of any pyramid is the sum of the lateral area and the area of
the base. (S.A = L.A + B)

SELF – CHECK TEST

Direction: Match column A with column B. Write the letter of your answer in your answer sheet.

A B

1. The base is a polygon and its faces are triangles. A. Rectangular Prism

2. It is composed of two rectangular bases and four rectangular B. Cone

lateral faces.

3. A spatial figure having a circular base and one vertex. C. Pyramid

4. A spatial figure which is perfectly round and symmetrical D. Cylinder

Solid figures with no edge and vertex.

5. A spatial figure with 2 circular bases, no edge and no vertex. E. Triangular Prism

f. Sphere
EVALUATION ACTIVITIES

Direction: Write T if the statement is true and F if it is false. Write your answer on your answer sheet.

________1. All faces of a cube are squares.

________2. A prism is a polyhedron with no congruent bases.

________3. A pyramid has no vertex.

________4. Solids have no flat surface.

________5. A cylinder is a two-dimensional solid figure with two congruent circular base that are
parallel.

References
Perez, M. (2020). 21st Century MATHletes 6. Manila: GDP TEXTBOOKS.