Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Comprehensive lesson notes on solid and plane geometry for the technical competency enhancement program 1 offered by the department of civil engineering. The notes cover topics such as polygons, triangles, quadrilaterals, circles, and polyhedrons, including their properties, formulas, and sample problems. The document also includes rules for two chords, two secants, and secant-tangent, as well as spherical components and sample problems.
Typology: Exercises
1 / 7
This page cannot be seen from the preview
Don't miss anything!
After careful study of this lesson, students should be able to:
Polygon โ a plane figure with three or more angles.
๐๐ข๐ ๐๐ ๐ผ๐๐ก๐๐๐๐๐ ๐ด๐๐๐๐๐ : ๐
๐
= 180ยฐ (๐ โ 2 )
๐๐ข๐ ๐๐ ๐ธ๐ฅ๐ก๐๐๐๐๐ ๐ด๐๐๐๐๐ : ๐
๐
= 360ยฐ
๐
2
2
4 tan (
Regular Polygon โ angles are equal and sides are equal
Similar Polygon โ two polygons are similar if angles are equal and sides are
proportional
Convex Polygon โ having each interior angle less than 180
o
Concave Polygon โ having an interior angle greater than 180
o
than the third side.
2
2
2
Quadrilateral Area
Rectangle ๐ฟ ร ๐
Square ๐
2
Parallelogram 0. 5 (๐
1
)(๐
2
)(๐ ๐๐๐)
Rhombus 0. 5 (๐
1
)(๐
2
)
Trapezoid
โ
2
(๐
1
2
)
Circle ๐๐
2
Cyclic Quadrilateral โ quadrilateral whose vertices lie on the circumference of a circle.
โฒ
1
2
General Quadrilateral
1. Circle Circumscribed about a Circle
โ(๐๐+๐๐)(๐๐+๐๐)(๐๐+๐๐)
4 ๐ด
๐๐ข๐๐
๐ด
๐๐ข๐๐
= โ
๐+๐+๐+๐
2
Polyhedrons โ solids whose faces are polygons (3D)
Regular Polyhedrons โ are those solids with all its faces identical regular polygons.
There are only five known regular polyhedrons: tetrahedron, hexahedron, octahedron,
dodecahedron, and icosahedron.
Polyhedron Volume Surface Area
Prism ๐ด
๐ต
โ 2 ๐ด
๐ต
Cylinder ๐ด
๐ต
โ 2 ๐๐
2
Pyramid (
1
3
)๐ด
๐ต
โ
๐ด
๐ต
Cone (
1
3
)๐ด
๐ต
โ
๐๐
2
Sphere (
4
3
) ๐ด
๐ต
โ
4 ๐๐
2
Frustum
(
โ
3
) (๐ด
1
2
โ
๐ด
1
๐ด
2
) ๐ด 1
๐ด 2
๐ฟ๐๐ด
Truncated Prism ๐ด
๐ต
โ
๐๐ฃ๐
๐ด 1
๐ด 2
๐ฟ๐๐ด
Spherical Components
2
2
2
2
3
2
