AREA - is the quantity that expresses the extent of a two-dimensional surface or shape, or planar lamina, in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat.[1] It is the two-dimensional analog of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept). Example : A square is a regular polygon with four sides. It has four right angles and parallel sides. To calculate the area of a square, multiply the base by itself, which can be expressed as side × side. If a square has a base of length 8 inches its area will be 8 × 8= 64 square inches Area of a square is given by: A = a2 where a = length of side Perimeter of a square = 4a Diagonal of a square = (a)(sqrt(2)) or 1.414 (a) Example 1: Find the area of a square of side length 15 m Solution: Area of a square = a2 = 152 = 225 m2 Example 2: Calculate the area of square, where the square has 35cm side’s length. Solution: Area of square is defined by a × a. Area = 35 × 35 Area = 1225cm Example 3: What is the area of a square field, if its perimeter is 32 yd? Solution: The perimeter of the square field = 32 yd and since the perimeter of a square is given by P = 4s, where s is the length of the side. We can easily determine the length by isolating s from the formula above: s = P/4 = 32 / 4 = 8 yd The area of the square field = s × s Substitute the value of s, we have: Area = 8 × 8 = 64 yd2 The area of the square field is therefore 64 yd2. VOLUME - is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains.[1] Volume is often quantified numerically using the SI derived unit, the cubic metre. The volume of a container is generally understood to be the capacity of the container, i. e. the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces. Example : Example 1 : Vijay`s window box is a cuboid of length 1 m , width 20 cm and height 30 cm. Work out its volume. First of all make all the units centimeters 1 m = 100 cm, so the volume is 100 x 20 x 30 = 60,000 cm³ The volume of the window box is 60,000 cm³ Example 2 : Igor`s working out how many cubic meters of concrete he`ll need for his patio. It will be 2 meters wide and 8 meters long and he needs to make it 10 cm deep. How much concrete will he need? First of all make all the units meters 10 cm = 0.1 m, so the volume is 8 x 2 x x 0.1 = 16 x 0.1 = 1.6 m³ Example 3 : Bonny has a rectangular garden pond 2 m long and 1 m wide. She wants to fill it to depth of 30 cm. How many liters of water will she need? First of all make all the units centimeters 200 x 100 x 30 = 600,000 cm³ Remember that 1 liter = 1,000 cm³ 600,000 ÷ 1,000 = 600 Bonny will need 600 liters of water CAPACITY - The capacity of a container is the volume of liquid that can fit inside the container. For example, the capacity of a hot water tank is the volume of water that can fit inside the tank. The capacity of a petrol tank is the volume of petrol that can fit inside the tank. The standard units often used for capacity are the liter (L) and the milliliter (mL). 1000 mL = 1L A container with an inner volume of 1 cm³ will hold 1 mL of liquid. That is: 1 mL = 1 cm³ We also use the units called kilolitre (kL) and even megalitre (ML). 1 kL = 1000 L 1 mL = 1 000 000 L Note : 1 mL = 1 cm³ 1 L = 1000 mL = 1000 cm³ Example 1 : Express 4 L in mL. Solution: 1 L = 1000 mL 4 L = 4 x 1000 mL = 4000 mL Example 2 : Express 6500 mL in L. Solution : 1000 mL = 1L 6500 mL = 6500 / 1000 L = 6.5 L Example 3 : Express 3.6 L in cm³ Solution : 1 L = 1000 mL = 1000 cm³ 3.6 L = 3.6 x 1000 cm³ = 3600 cm³ PERIMETER = is a path that surrounds a two-dimensional shape. The word comes from the Greek peri (around) and meter (measure). The term may be used either for the path or its length - it can be thought of as the length of the outline of a shape. The perimeter of a circle or ellipse is called its circumference. Examples Example 1 : Find the perimeter of a triangle with sides measuring 5 centimeters, 9 centimeters and 11 centimeters. Solution: P = 5 cm + 9 cm + 11 cm = 25 cm Example 2 : A rectangle has a length of 8 centimeters and a width of 3 centimeters. Find the perimeter. Solution 1: P = 8 cm + 8cm + 3 cm + 3 cm = 22 cm Solution 2: P = 2(8 cm) + 2(3 cm) = 16 cm + 6 cm = 22 cm Example 3 : Find the perimeter of a square with each side measuring 2 inches. Solution: P = 2 in + 2 in + 2 in + 2 in = 8 in Resources : mathgoodies/lessons/vol1/perimeter.html en.wikipedia.org/wiki https://google.ph/?gfe_rd=cr&ei=RkgBVNrbBIeY-QO3oIHgDw&gws_rd=ssl
Posted on: Sat, 30 Aug 2014 03:43:17 +0000
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