perimeter and area

Calculate The perimeter and area of triangle and Rectangular Shape

A= l x w

Formula of Rectangle Area

Formula of Perimeter

P = 2 (w + l)

l

w w

l

Perimeter of Rectangle= w+w+l+lPerimeter of Rectangle= 2w+2l

Perimeter of Rectangle= 2(w+l)

Exercise1. Calculate the perimeter and the area of

rectangles with the following measures: a. Length is 17 dm and width is 7 dm. b. Length is 20 mm and width is 5 mm. c. Length is 25 m and width is 8 cm.

a c t i iv t y 2

D

A B

C

AB=….cm ∠AOB =.......° BC=….cm ∠BOC =.......°CD=….cm ∠COD =.......°AD=….cm ∠DOA =.......°AC=….cm ∠OAD =.......°BD=….cm ∠OBA =.......°

∠OCB =.......°∠ODC =.......°∠OAB =.......°∠OBC =.......°∠OCD =.......°∠ODA =.......°

Properties

1. The opposite sides are parallel. 2. All of the angles are right angles. 3. The diagonals are equal and bisect each other. 4. All the sides are equal. 5. The diagonals 1. The opposite sides are

parallel. 2. All of the angles are right angles. 3. The diagonals are equal and bisect each other. 4. All the sides are equal. 5. The diagonals bisect the angles. 6. The diagonals cross perpendicularly.

Definition

Based on those properties, we can say that a square is a

rectangle with 4 equal sides and one of its angle is right

angle.

Formula of The Area

A = s x s

Suppose you have a room. The room floor is in a square shape. The floor will be covered with square tiles.

Formula of Perimeter

P = 4 s

s

s

s

sPerimeter of square = s + s + s + s

Perimeter of square = 4s

Rhombus

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ii ot n

If both diagonals of a quadrilateral are perpendicular and bisect each other, then it is

called a rhombus.

Rhombus is a quadrilateral with four equal sides.

We can also say

a c t i iv t y 3

1. Make two congruent isosceles triangle

2. Coincide the base of both triangles

Properties

All sides are equal Opposite sides are parallel Vertical angles are equal The diagonals bisect the angles Both diagonals are perpendicular and

bisect each other Diagonals bisect the rhombus or they

are the axis lines The sum of the two adjacent angles is

180°

Formula of The Area

The area of rhombus= Area of 𝜟ACD + Area of ACB

The area of rhombus= ½ (AC)(a) + ½ (AC)(a)

The area of rhombus= ½ (AC)(a+a)

The area of rhombus= ½ (AC)(2a)

The area of rhombus= ½ (d1)(d2)

a

a

C

D

A

B

O

The area of a rhombus is equal to a half of the product of the

diagonals.

Formula of Perimeter

The perimeter of a rhombus is four times the length of the sides.

Suppose P is the perimeter of a rhombus with the length of side s, then

P = 4 × s

Exercise

The area of rhombus ABCD is 180 cm2 . The length of diagonal AC is 24 cm. what is the length of BD?

Kite

Kite is a quadrilateral with diagonals perpendicular to each other and one of the diagonals bisects the other.

a c t i iv t y 4

1. Make two isosceles triangle which has the same base

2. Coincide the base of both triangles

Properties

1. Two pairs of the sides close to each other are equal, namely AB = AD and BC = DC.

2. One pair of backside angles is equal, that is ∠ABC = ∠ADC.

3. One of the diagonals bisects the kite, that is ΔABC = ΔADC or AC is the axis of symmetry.

4. Diagonals are perpendicular to each other and one of the diagonals bisects the other, that is, AC ⊥ BD and BE = ED .

B

C

D

A

Formula of The Area

The area of kite= Area of 𝜟ACD + Area of ACB The area of kite= ½ (AC)(a) + ½ (AC)(b) The area of kite= ½ (AC)(a+b)

The area of kite= ½ (d1)(d2)

a

b

C

D

A

B

O

The area of a kite is equal to a half of the product of the

diagonals.

Formula of Perimeter

P = AB + BC + CD + DA= x + x + y + y= 2x + 2y= 2(x + y)

C

D

A

B

y y

x x

Exercise Find the area of a kite with its diagonal:a. 8cm and 12cmb. 9cm and 16cmc. 15cm and 18cmd. 13cm and 21cm

Formula of The Area

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1. Make a parallelogram and give the identity the base and the height!

2. Cut on line DE and move the triangle AED such that side ad coincide side BC, ∠A becomes supplement of ∠B, and ∠D becomes complement of ∠C. What shape do you get?

B

D C

A

Height (t)

Base (a)

3. What can you say about the area of the rectangle and the area of the initial parallelogram? Are they the same?

4. What is the area of a rectangular?5. What can you conclude about the area of

parallelogram?

The Area and Perimeter of Parallelogram The area of parallelogram is defined as

product of the base and the height. The perimeter of a parallelogram is defined

as twice of two adjacent sides of the parallelogram.

If a parallelogram has area A, base a, adjacent side of a is b and height t, then A = a × t P = 2 (a + b)

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