Everything Maths Grade 11

CHAPTER 16. GEOMETRY 16.3

3.

A triangular pyramid is placed on top of a triangular

prism. The prism has anequilateral triangle of side

length 20 cm as a base, and has aheight of 42 cm.

The pyramid has a height of 12 cm.

(a) Find the total volume of the object.

(b) Find the area of eachface of the pyramid.

(c) Find the total surfacearea of the object.

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(1.) 012u (2.) 012v (3.) 012w

16.3 Similarity of Polygons

In order for two polygons to be similar the following must be true:

1. All corresponding angles must be congruent.


2. All corresponding sides must be in the same proportion to each other.Refer to the picture below:
   this means that the ratioof side AE on the large polygon tothe side P T on the small polygon
   must be the same as theratio of side AB to side P Q, BC/QR etc. for all the sides.

B

D C

A

E

T

S R

Q

P

If

1.Aˆ =Pˆ;Bˆ =Qˆ;Cˆ =Rˆ;Dˆ =Sˆ;

Eˆ =Tˆ

and

2.ABPQ=BCQR=CDRS=DEST=EATP

then the polygons ABCDE and

P QRST are similar.