Math-A Lesson 10-3: Area of: -Triangles -rectangles -circles -trapezoids and Surface Area of: -Rectangular Prisms
Describe the idea of area. Area attempts to answer the question how big is it? The area of this square is.? 1 inch 1 inch area = length * width area = (1 inch)(1 inch) area 1inch area = 1 square inch When we ask for an area, we really mean, how many 1 inch x 1 inch squares will fit in the area.
1 inch The area of this circle is.? how many 1inch squares will fit in the circle. 1 inch area less than 4 inch Will all those extra corners make up 1 sq. inch? No. They make up slightly less than 1 sq. inch. area slightly more than 3inch area 3.148 inch
What is the definition of pi? distance around the circle distance across the circle Circumference diameter C D C D Circumference radii C r C r
The area of this circle is.? area r What is the area of the circle given by the equation? 16 x ( y area 16 )
.7 inch The area of this circle is.? A r Is the given dimension a radius? area.7 5.73 in If decimal dimensions are given in the problem, it is OK to have a decimal answer. If the problem says to use 3.14 for pi, DO NOT use the pi button on your calculator; use 3.14.
The area of this triangle is.? 4 in A 1 *base*height 3 in Base (of a triangle): any side of the triangle. height (of a triangle): the perpendicular distance (altitude) from any vertex of the triangle to its opposite side. height (of a triangle) is the same at its altitude.
The altitude of a triangle. A 1 *base*height Area formula: requires the use of matching altitudes and sides.
Area ΔABC =? Area 0.5*base*height C Drop an altitude to the longest side. a=14 h b=3 sin 33.6 = h 3 h 3 33.6º B c=5 33.6º A 3 (sin 33.6) = h h = 1.7 Area ΔABC = 0.5 5 (1.7) Area ΔABC = 159.1 units
The width of a rectangle is feet. The length is twice the width. What is the perimeter of the rectangle? W L L W w = L = w substitution L = = 4 P L w substitution rectangle P rect. = 4 + () P rect. = 1 ft
The width of a rectangle is 3 feet. The length is four times the width. What is the area of the rectangle? w = 3 L = 4w substitution L = 4 3 = 1 Area l * w substitution rectangle A rect. = (1 ft)(3 ft) A rect. = 36 ft W L L W
If the width of a rectangle is twice the length, and the perimeter is 90 feet, what is the area? w = L P substitution rect. = 90 ft P L w rectangle W L L W 90 = L + (L) solve for L 90 = 6L L = 15 w = 30 substitution w = L substitution A = L w A rect. = (15 ft)(30 ft) A rect. = 450 ft
The area of a trapezoid is the average of the two bases times the height. 1 A b1 b h One base has a length of 6 feet. The other base is three times as long. If the area of the trapezoid is 75 square feet, what is the height? b 1 = 6 ft substitution b = 3 6 ft = 18 ft b = 3b 1 A = 75 ft substitution A = 0.5 b 1 + b h 75 = 0.5 6 + 18 h 75 = 1h solve for h h = 6.5 ft b 1 b h
What does surface area mean? Surface area: The area of the surface of the shape. Why would this information be important? Helps you to know how much material you need to build, paint, or cover the item.
A Solid : a three-dimensional shape. Prism: a solid that has two parallel polygonal bases and planer ( flat ) sides. Prisms are named based upon the shape of their bases. If the sides intersect the base at a right angle, we include that in the name: Right Rectangular Prism Lateral Area: the total area of the sides.
Build a net (flatten out the box ). Symbolically we could say: Surface area prism + +
What is the surface area of the prism? 4 in 6 in 6 in 4 in 6 in 10 in 10 in 6 in Surface + + area prism 6 in SA = 4 10 + 6 10 + (4 6)
Area of a Rectangle The length of a rectangle is 4 more than 3 times its width. The area of the rectangle is 00 square inches. What is the length and width of the rectangle? Area = L * W L = 3W + 4 A = 00 Using substitution: 00 = (3W + 4) * W Solve by graphing. width length
Area of a Rectangle Area = L * W L = 3W + 4 A = 00 Using substitution: 00 = (3W + 4) * W y x( 3x 4) 00 Find the zero of the equation. Solve by graphing. Get into zero equals form 0 = W(3W + 4) 00 Let x = width 0 x(3x 4) 00 x = width = 7.53 inches
Area of a Rectangle Area = L * W L = 3W + 4 y A = 00 Using substitution: 00 = (3W + 4) * W x( 3x 4) 00 Find the zero of the equation. Using substitution: L = 3W + 4 L = 3(7.53) + 4 L = 6.59 inches Check: 00 = L*W Check: 00 = (6.59)(7.53) x = width = 7.53 inches