# Find the Area of a Shape

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Last updated 6 years ago

Discipline:
Math
Subject:
Geometry
Grade:
5,6   FInd the Area of a Shape

Rachel CaldwellTuesday 5:00

CCSS.MATH.CONTENT.6.G.A.1Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

FInd the Area Video

The area of a polygon is the number of square units inside that polygon. Area is 2-dimensional like a carpet or an area rug. A triangle is a three-sided polygon. We will look at several types of triangles in this lesson. To find the area of a triangle, multiply the base by the height, and then divide by 2. The division by 2 comes from the fact that a parallelogram can be divided into 2 triangles. For example, in the diagram to the left, the area of each triangle is equal to one-half the area of the parallelogram.Since the area of a parallelogram is A = b x h, the area of a triangle must be one-half the area of a parallelogram. Thus, the formula for the area of a triangle is: or where b is the base, h is the height and · means multiply. The base and height of a triangle must be perpendicular to each other. In each of the examples below, the base is a side of the triangle. However, depending on the triangle, the height may or may not be a side of the triangle. For example, in the right triangle in Example 2, the height is a side of the triangle since it is perpendicular to the base. In the triangles in Examples 1 and 3, the lateral sides are not perpendicular to the base, so a dotted line is drawn to represent the height. Example 1:Find the area of an acute triangle with a base of 15 inches and a height of 4 inches.Solution: A = · (15 in) · (4 in) A = · (60 in2) A = 30 in2Example 2:Find the area of a right triangle with a base of 6 centimeters and a height of 9 centimeters.Solution: A = · (6 cm) · (9 cm) A = · (54 cm2) A = 27 cm2Example 3:Find the area of an obtuse triangle with a base of 5 inches and a height of 8 inches.Solution: A = · (5 in) · (8 in) A = · (40 in2) A = 20 in2 Example 4:The area of a triangular-shaped mat is 18 square feet and the base is 3 feet. Find the height. (Note: The triangle in the illustration to the right is NOT drawn to scale.)Solution:In this example, we are given the area of a triangle and one dimension, and we are asked to work backwards to find the other dimension. 18 ft2 =· (3 ft) · h Multiplying both sides of the equation by 2, we get: 36 ft2 = (3 ft) · h Dividing both sides of the equation by 3 ft, we get: 12 ft = h Commuting this equation, we get: h = 12 ftSummary:Given the base and the height of a triangle, we can find the area. Given the area and either the base or the height of a triangle, we can find the other dimension. http://www.mathgoodies.com/lessons/vol1/area_triangle.html

How to Calculate the Areaof a CircleThe area of a circle is π (Pi) times the Radius squared, which is written: A = π × r2Or, when you know the Diameter: A = (π/4) × D2Or, when you know the Circumference: A = C2 / 4πhttp://www.mathsisfun.com/geometry/circle-area.html

How to find the area of a square:The area of a square can be found by multiplying the base times itself. This is similar to the area of a rectangle but the base is the same length as the height.If a square has a base of length 6 inches its area is 6*6=36 square incheshttp://www.aaamath.com/exp78_x4.htm

Area FormulasArea CalculatorArea of Shapes Game

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