Area of Plane Figures

transcript

Richard B. PaulinoINRSF – Laoag City

A square with a side of 1 unit has an area of 1 square unit in symbol 1 unit2

Hence, the unit of measure used for measuring the area of a plane figure is square unit (unit2 )

Unit for Side Unit for AREA

cm cm2 (square centimeter)

m m2 (square meter)

ft ft2 (square feet)

– size of a surface or region.

- the number of square units to cover a surface or region.

AREA of a SQUAREHow many square units will be used to cover a square region whose side is 3 units long?

A = 3 units x 3 units

A = 9 square unitsA=9 units2

Where: s = side of a square

Let s be the side of a square then, A=s units x s units

AREA of a SQUARE

21 cm9.5 km

3.75 cm

18 in 31 ft17 dm

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Instruction: Find the area of each square.

AREA of a RECTANGLEHow many square units will be used to cover a rectangular region whose length is 4 units and width is 3 units long?

Area = 4 units x 3 units = 12 units2 The formula is:

Area =l × wwhere: w = width

l = length

A=12 units2

AREA of a RECTANGLEExample: What is the area of this rectangle?

The formula is:Area =l × w

where: w = widthl = length

We know that w = 4 cm and l = 5 cm, so: Area = 5 cm × 4 cm = 20 cm2

ACTIVITYArea of Rectangles

Instruction: Find the area of each rectangle.

130 cm

17 0 cm

Name:_______________________________ Score: ____Grade/section: ____________ Date: _____

ACTIVITY

Instruction: Find the area of each rectangle using the given measures. 1 l = 7 km ,w= 14 km 6. l = 2.6 cm , w = 5 cm 2. l = 7 cm , w = 1.5 cm 7. l = 21 ft , w = 12 ft 3. l = 18 yd , w = 9 yd 8. l = 3.75 ft , w = 4.5 ft 4. l = 9.5 in , w = 9 in 9. l = 31 mm , w = 23 mm

5. l = 13 km , w = 8 km 10. l = 11 dm , w = 6 dm

ACTIVITY AREA OF RECTANGLES

Instruction: Answer the following problems completely.1. The measure of a basketball court is 26 cm by 14 cm, find its area. Given: ____________________

Required:__________________Formula: __________________Equation/Number Sentence:__________________Solution/Answer: __________________________

2. Find the area of a baseball court with the measure of 90 ft by 60 ft. Given: ____________________

3 . One face of chalk box has a length 60 cm and its width is 30 cm, find its area. Given: ____________________

4. If the measure of a volleyball court is 50ft by 70 ft, what is its area. Given: ____________________

5. The measure of a fishpond is 26 m by 78 m, find its area. Given: ____________________

Name:_______________________________ Score: ____Year/section: ____________ Date: _____

ACTIVITY

Instruction: Answer the following problems completely. 6. Find the floor area of the gymnasium whose length and width is 65 m and 45 m respectively. 7. A badminton court has a measure of 27 m by 36 m, find its area.

8. Find the width of a rectangle with the area of 186 square yards and a length of 13 yards. 9. One dimension of rectangular pool table is 76 cm. Its area is 8664 cm2, find the other dimension. 10. The length of the base of the table in the canteen is 15 m and the length of the diagonal is 17 m. Find its area.

AREA of a Parallelogram

height

Height (h)

Base (b)

The formula is:Area =b × h

where: b = baseh=height

4)5 cm

8.5 cm

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Instruction: Find the area of each parallelogram.

AREA of a TRIANGLE

Height (h)

Base (b)Area of a Paralellogram

Area =b × h Area of a Triangle Area = ½ (Area of a Parallelogram)

Area = ½ (b × h)

AREA of a TRIANGLE

A = 3 units X 3 unitsA = 9 square units

A = 4 units X 3 unitsA = 12 square units

(9 square units)

4.5 square units)

the area of the rectangle

(12 square units)

6 square units

AREA of a TRIANGLE

(b x h) Where: b= baseh = height

Example

AREA of a TRIANGLE

5 m 5 m

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Area of a Trapezoid

b 1 b2

A = base x height

Height (h)

Area of a parallelogram

A = (b1 + b2) x h

Area of a trapezoid = ½ Area of a parallelogram

Area of a trapezoid = ½ (b1 + b2) x h

Example Find the area of trapezoid ABCD.

6 units

4 units

8 units

A = ½ h ( b1 + b2) = ½ ( 4) (8 + 6 ) = ½ ( 4 ) ( 14 ) A= 28 The area is 28 square units.

7.25 m

5 ft 3 ft 10 ft

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Instruction: Find the area of each trapezoid.

AREA of a CIRCLE

Radius (r)

C=2πr

1/2C=πr

base (b)= πr

height (h) = r

A = base x height

A = πr2x rπr

d = 6 cm

Example 1 The radius of a circle is 2 cm. Find its area.

Solution: A = r2 r=2 cm

3.14 (2)2 ●12.56 cm2 The area is 12.56 square cm.

Example 2 The diameter of a circle is 6 cm. Find its area.Solution: Step 1. Find the radius

Radius( r ) = diameter (d) divided by 2 r = 6 2 r = 3 cm The radius is 3 cm. ● Step 2. Find the area. A = r2

3.14 (3)2

3.14 (9) 28.26 cm2

The area is 28.26 cm2

Try this out Find the area of each circle with the given diameter or radius Use 3.14 for .

1. `radius = 5 cm2. radius = 1.5 mm3. diameter = 4 cm4. diameter = 12 dm5. radius = 4.6 m6. radius = 2.2 cm7. diameter = 4.8 dm8. diameter = 6.4 cm9. radius = 4.8 m10. radius = 3.4 dm

Let’s Summarize1. The area of a region is the number of square units

contained in the region.

2. A square unit is a square with a side 1 unit in length.The area (A) of a rectangle is the product of its length (l) and its width (w). A = lw

3. The area (A) of a square is the square of the length of a side (s). A = s2

4. The area (A) of a parallelogram is equal to the product of the base (b) and the height (h). A = bh

5. The area (A) of a triangle equals half the product of the base (b) and the height (h). A = ½ bh. Sometimes altitude is used instead of height.

6. The area (A) of a trapezoid is one half the product of the length of its altitude and the sum of the lengths of the two bases. A = ½ h (b1 + b1).7. A circle is a set of points in a plane that have the same distance from a given point in the plane. 8.The formula for the area of a circle with a radius of r and diameter of d units are: A = r2 and A = (d/2)2 respectively.Note: In all circles the ratio of the circumference to the diameter is always equal to the same number, represented by the Greek letter .

Area of Plane Figures

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