Last Updated: 16-21-2021 | Esoma-KE

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Last Updated: 16-21-2021 | Esoma-KE

- Opposite sides are equal
- Each interior angle is 90° and they all add up to 360°
- Diagonals are equal
- Diagonals bisect each other but NOT at right angles

= L + L + W + W

= 2L + 2W or 2(L+W)

A = L × W

P = 2(L+W) (See above for the complete formula)

P = 2(14 + 7) cm

P = 2(21) cm

P = 42 cm (Do not forget the units)

A = L × W

A = 14 × 7

A = 98cm

- All sides are equal
- Opposite sides are parallel
- Each interior angle is a right angle (90°)
- The interior angles total up to 360°
- Diagonals bisect each other at right angles.
- Diagonals measure the same length and bisect interior angles.

= L + L + L + L

= 4L

A = L

P = 4L (See above for the complete formula)

P = 4 x 12

P = 48 cm (Do not forget the units)

A = L × L or L

A = 12 × 12

A = 144cm

- Opposite sides are equal and parallel
- Opposite angles are equal
- Diagonals bisect each other
- Diagonals are not equal
- Adjacent angles are supplementary (add up to 180°)

A = b x h

- All sides are equal
- Opposite sides are parallel
- Opposite angles are equal
- Diagonals bisect each other at 90°
- Diagonals bisect the interior angles

A = b x h

- The sum of the interior angles is 360°
- Has a pair of parallel lines which are not of the same length
- Has a perpendicular height joining the two parallel lines

A = ½ × (a + b) × h

A = ½h (a + b)

A = ½h (a + b)

A = ½ x 8 x (10 + 18)

A = ½ x 8 x 28

A = 112cm

- a
^{2}+ b^{2}= c^{2} - a
^{2}= c^{2}- b^{2} - b
^{2}= c^{2}- a^{2}

- All sides are equal
- All angles are equal
- The sum of interior angles is 180°
- Each angle measures 60°

- Only two sides are equal
- Base angles are equal

P = a + b + c

Area = ½ b x h

A = π x r x r

A = πr

(π =

Diameter = r + r

P = π x 2r

P = πd or 2πr

(π =

A = (π x r x r) ÷ 2

A =

Perimeter = (π x diameter) ÷ 2 + Diameter

Diameter = r + r

P =

A = (π x r x r) ÷ 4

A =

TSA = 2πr

V = πr

V = πr

Total Surface Area = Total Area of all Six Faces

= 6 x L x L

= 6L^{2} - if closed

= 5L^{2} - if open on one end

= 6 x L x L

= 6L

= 5L

V = length x width x height

V = L x w x h

Total Surface Area = Total Area of all Six Faces

= 2 (L x W) + 2 (L x H) + 2 (W x H) - if closed

= L x W + 2 (L x H) + 2 (W x H) - if open on one end

= 2 (L x W) + 2 (L x H) + 2 (W x H) - if closed

= L x W + 2 (L x H) + 2 (W x H) - if open on one end

Total Surface Area = Total Area of all five Faces of the Prism

= TSA of 2 Triangles and TSA of 3 Rectangles

= TSA of 2 Triangles and TSA of 3 Rectangles

Complex shapes are made up of two or more common shapes.

To find the perimeter and surface area, you will have to apply different formulas and sum them to get the total.

For Instance, look at the objects below:

#### Example 1

#### Calculating the Perimeter

How many common shapes make up this object?

There are 2: A Rectangle and a Semi-circle.

**Perimeter of the semi circle**

P =^{1}/_{2}πd

P =^{1}/_{2} x ^{22}/_{7} x 21

P = 33 cm

**Perimeter of the 3 sides of the rectangle**

P = L + W + L

P = 33 + 21 + 33

P = 87cm

**Total Perimeter:**

T.P = 33 + 87

**120 cm**
#### Example 2

#### Calculating the Perimeter

How many common shapes make up this object?

There are 4 Semi-circles.

**Perimeter of the small semi circles**

P =^{1}/_{2}πd

P =^{1}/_{2} x ^{22}/_{7} x 14

P = 22 cm (For 1 semi circle)

22cm + 22cm

= 44 cm

**Perimeter of the larger semi circles**

P =^{1}/_{2} x ^{22}/_{7} x 42

P = 66 cm (For 1 semi circle)

66 + 66

= 132 cm

**Total Perimeter:**

T.P = 44 + 132

**176 cm**

To find the perimeter and surface area, you will have to apply different formulas and sum them to get the total.

For Instance, look at the objects below:

There are 2: A Rectangle and a Semi-circle.

P =

P =

P = 33 cm

P = L + W + L

P = 33 + 21 + 33

P = 87cm

T.P = 33 + 87

There are 4 Semi-circles.

P =

P =

P = 22 cm (For 1 semi circle)

22cm + 22cm

= 44 cm

P =

P = 66 cm (For 1 semi circle)

66 + 66

= 132 cm

T.P = 44 + 132

2000 revolutions = 2000 πd;

= (2000 x

= 3 520m

We convert m to km (1000m = 1km)

= 3520 ÷ 1000

=

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