All about those Triangles and Circles 1BUTYPES OF TRIANGLES Triangle - A three-sided polygon. The sum of the angles of a triangle is 180 degrees. Isosceles Triangle - A triangle having two sides of equal length. Scalene Triangle - A triangle having three sides of different lengths. Acute Triangle- A triangle having three acute angles or angles less than 90 degrees. Obtuse Triangle- A triangle having an obtuse angle. One of the angles of the triangle measures more than 90 degrees.
Right Triangle - A triangle having a right angle. One of the angles of the triangle measures 90 degrees. The side opposite the right angle is called the hypotenuse. The two sides that form the right angle are called the legs. A right triangle has the special property that the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse. This is known as the Pythagorean Theorem. Equilateral Triangle - A triangle with three equal segments or sides. An equilateral triangle is a HtriangleH with all three sides of equal length a, corresponding to what could also be known as a "regular" triangle. An equilateral triangle is therefore a special case of an Hisosceles triangleh having not just two, but all three sides equal. An equilateral triangle also has three equal 60 HanglesH. Equiangular- A triangle with three equal angles of 60 o. ISOCELES An isosceles triangle is a HtriangleH with (at least) two equal sides. In the figure above, the two equal sides have length b and the remaining side has length a. This property is equivalent to two angles of the triangle being equal. An isosceles triangle therefore has both two equal sides and two equal angles. The name derives from the Greek iso (same) and skelos (HlegH).
2BUFINDING THE PERIMETER OF A TRIANGLE To find the perimeter (total distance) around a triangle, add up all of the sides of the triangle. 3BPerimeter = Side1 + Side2 + Side3 Example: 7in 12.2 in C 10 in Perimeter = Side1 + Side2 + Side3 Perimeter = 7 in + 10 in + 12.2 in = 29.2 in 0BPythagorean Theorem If two of the sides of a right-angle triangle are known, then a formula called Pythagorean Theorem can be used to calculate the third side. RIGHT-ANGLE TRIANGLE A right triangle has one right-angle. The side opposite the square of any right angle triangle is called the hypotenuse. To find the hypotenuse, use the formula, where c = the hypotenuse, a = the base of the triangle and b = the height of the triangle. The square is the 90 angle in the right triangle.
Example: A right angle triangle has a height of 5 cm and a base of 3 cm, find the hypotenuse. When the hypotenuse and one side of a right-angle triangle is known, you can find the length of the unknown side by using the Pythagoras theorem. To do this, follow the steps below. 1. Square the hypotenuse. 6 6=36. 2. Square the other known side. 5 5 = 25. 3. Subtract the known smaller side from the hypotenuse 36-25=11 4. Square root the result of the subtraction. 11 = 3.32 rounded to the nearest hundredth. 3.32 is the length of the unknown side. Examine the example solution below:
4BUFINDING THE AREA OF A TRIANGLE Height Height Base Base Area = ½ * Base * Height Example 1: If the Base of a triangle = 5 ft, and the height = 3 ft, what is the area of the triangle? Area = ½ * 5 * 3 = 7.5 sq ft Example 2: If the Area of the triangle = 16 sq ft. and the Height = 4 ft, what is the length of the Base? Area = ½ * base * height 16 = ½ * base * 4 ft 16 = 2 * base 16/2 = base 8 ft = base Do the following problems: 14 in 22.8 in 1) The triangle above is a right triangle. What is the perimeter of the triangle above? (1) 27.8 (2) 54.8 (3) 58.8 (4) 62.8 (5) 68.3 In the same triangle above, what is the area? (1) 96 sq in (2) 108 sq in (3) 117 sq in (4) 126 sq in (5) 154 sq in
33 in 50.3 in 2) In the above triangle, if the perimeter = 121.32 in, the base =? (1) 38 1/5 (2) 38 2/9 (3) 38 1/50 (4) 38 2/103 (5) 38 4/17? in The following Right Triangle applies to problems 3 9: A C B 3) If A = 7 and B = 9, what does C =? (1) 10.3 (2) 11.4 (3) 12.6 (4) 14.8 (5) 16.2 4) If A = fifteen and twenty-six hundreths and B = nineteen and nine hundreths, what does C =? (1) About twenty-four and forty-four hundredths (2) About thirty-two and sixteen hundredths (3) About thirty-seven and twenty-two thousandths (4) About forty-one and seven tenths (5) About ninety-seven and two hundredths 5) If A = 45 1/8 and B = 52 3/7, what does C =? (1) About 27 15/100 (2) About 32 33/100 (3) About 69 17/100 (4) About 75 19/100 (5) About 81 23/44 6) If C = 154 and B = 98, what does A =? (1) About 108 (2) About 119 (3) About 157 (4) About 206 (5) About 216
A B 19 8/11 in 11 2/5 in 7) In the above triangle, what is the area of the triangle? (1) About 97 ¾ sq in (2) About 100 ¼ sq in (3) About 108 ¾ sq in (4) About 112 ½ sq in (5) About 123 ¼ sq in 8) For problem #7, if the triangle were an equalateral triangle, what would side A equal? (1) 11 1/4 in (2) 11 17/23 in (3) 11 12/30 in (4) About 11.37 in (5) About 11.05 in 9) For problem #7, if the triangle were an equalateral triangle, what would the perimeter of the triangle equal? (1) 11 2/5 in (2) 11 3/5 in (3) 34 1/5 in (4) 34 2/5 in (5) 34 2/9 in 10) For problem #7, if the triangle were an equalateral triangle, what would the total area of 17 of the triangles be? (1) 1,684.25 sq in (2) 1,776.5 sq in (3) 1,805.75 sq in (4) 1,887.25 sq in (5) 1,912.5 sq in 11) One side of a triangle is 22 3/8% of the total perimeter. Another side is 38% of the total perimeter. If the total perimeter is 155 1/5 ft, how long is the remaining side of the triangle? (1) 61 4/5 in (2) 61 499/1000 in (3) 61 249/500 in (4) 61 15/89 in (5) 61 47/52 in 12) The total perimeter of nine equalateral triangles is 837 feet. What is the length of one side of these triangles? (1) 31 4/5 in (2) 31 2/9 in (3) 31 4/5 in (4) 31 3/16 in (5) 31 in
5BANSWER THE FOLLOWING PROBLEMS 1) Circumference of a circle is 180 ft. What is its area? (1) About 2,745 sq ft (2) About 2,601 sq ft (3) About 2,578 sq ft (4) About 2,433 sq ft (5) About 2,319 sq ft 2) Circumference of a circle is 250 ft. What is its area? (1) About 4,691 sq ft (2) About 4,712 sq ft (3) About 4,758 sq ft (4) About 4,810 sq ft (5) About 4,974 sq ft 3) Area of a circle is 1,460 sq ft. What is its circumference? (1) About 122 ft (2) About 136 ft (3) About 154 ft (4) About 175 ft (5) About 200 ft 4) Area of a circle is 1,875 sq ft. What is its circumference? (1) About 122 ft (2) About 136 ft (3) About 154 ft (4) About 175 ft (5) About 200 ft 5) Mary is building 7 identical circular gardens. If the area of each will be 58 sq ft, how much fencing must she buy? (1) About 125 ft (2) About 140 ft (3) About 152 ft (4) About 174 ft (5) About 189 ft