math 202 july 27 lesson

July 27July 27

Note to students• Remedial classes were postponed

yesterday. It will resume later

• Read everything that will be flashed on screen. Oral recitation questions are also given here.

• Questions are of random difficulty. It is expected that you have read your book and at least answered the exercises in the book.

RecapRecap

Perimeter• It is the distance (measure) of the

outer side of a polygon.

• In order to find the perimeter, add up the length of each sides of the figure.

Perimeter• If there are different units of length,

convert it to what is asked.

• If there is an unknown side, simply subtract the partial sum of the sides to the given perimeter.

Oral Recitati

on

Perimeter

1. 4.5 m

5 m

6 m

4 m

= 39 m

Perimeter2.

4 m

5 m= 18 m

Perimeter

3.

7.5 dm

2 dm2.5 dm

2 dm

2 dm

2.5 dm

= 37 dm

Perimeter

4. Find the perimeter of an isosceles triangle with base 8 dm and equal sides 12.5 dm.

= 33 dm

Perimeter

5. Find the perimeter of a regular icosagon if the side is 2 cm.

= 40 cm

Perimeter

6. The perimeter of a regular octagon is 60 mm. what is the measure of the sides?

= 7.5 mm

AreaArea

Area

1. In Elementary, what are the polygons that have formulas in finding its area?

- Square, Rectangle, Parallelogram, Rhombus, Triangle, Trapezoid

2. What will you do if the given figure doesn’t have a formula for its area?

- Divide it into triangles, rectangles, parallelograms, or trapezoids

Area

3. How will you find the area of a divided figure?

- By summing up the areas of all divided parts of which can be calculated easily by

the formulas

4. What will you do if the given figure has an unknown side but has a given area?

- Equate the area of the given figure to the formula and substitute any given part. Ex

ExampleThe area of a rectangle is 60 cm2. If the width is 6 cm, what is the length of the square?<==

A = lw = (6 cm)

Area

5. If you are unsure whether the figure is square or rectangle, what is the safest formula to use?

A = lw

6. What is Heron’s formula in finding the area of triangle?

s = A =

Heron’s (or Hero’s) Formula

- Named after Heron of Alexandria- This is the formula in finding the

area of a triangle when all sides are given.

- s is called semi-perimeter

ExampleA Triangle has sides with 3 cm, 4 cm, and 5 cm measures. What is the area?

s = 6 cm

A = =

= 6 cm2

<==

Area

7. What is the Pythagorean theorem and when do we use it?

8. To which polygon can it be applied?

- Right Triangles only

Pythagorean TheoremThe square of the hypotenuse is equal to the sum of the squares of the legs.

(leg 1) a

b (leg 2)

c (hypotenuse)

a2 + b2 = c2

ExampleThe legs are 4 cm and 3 cm, find the measure of the hypotenuse.

a2 + b2 = c2

32 + 42 = c2

9 + 16 = c2

25 = c2

5 = c<==

Area

9. Find the area of the pentagon

10 cm

5 cm

8cm

12cm

= 113 cm2

Area

10. The first diagonal is 37 cm and the other is 160 mm.

d1 d2

= 296 cm2 or 59200 mm2

Area

11. The area of a parallelogram is 120 square centimeters. What is the height of the parallelogram if the base is 10 cm?

= 12 cm

Area

13. Find the value of the unknown. A = 231 cm2

= 14 cm

a cm

12 cm

21 cm

Area

12. Find, in hectares, the area of the figure shown below. Give your answer correct to 2 decimal places.

286 mm

210 mm

30 cm

24 cm

30 cm

= 234.6 cm2

Area

14. Find the area if AB = 12 m, AD = 16 m, and triangle CDE is 24 m2

= 216 m2

E C

DA

B

Area

15. Find the area of the triangle

= 14.7 cm2

5 cm 7 cm

6cm

AssignmentPages

124-125 #s 3-4136 A (1-2), B (1-2)137 C (1-2), A (1-2)