Introduction
Welcome to our blog post on "11.5 practice a geometry answers". In this article, we will provide detailed answers and explanations for the practice questions in section 11.5 of your geometry textbook. Whether you are a student looking for help with your homework or a teacher in need of additional resources, we've got you covered. Let's dive in!
Question 1: Find the area of a triangle
To find the area of a triangle, you can use the formula A = 1/2 * base * height. The base of the triangle is 10 cm and the height is 6 cm. Plugging in these values into the formula, we get:
A = 1/2 * 10 cm * 6 cm
A = 30 cm²
Therefore, the area of the triangle is 30 cm².
Question 2: Calculate the circumference of a circle
The circumference of a circle can be found using the formula C = 2πr, where π is a mathematical constant approximately equal to 3.14 and r is the radius of the circle. In this question, the radius is given as 5 cm. Plugging in these values into the formula, we get:
C = 2π * 5 cm
C ≈ 2 * 3.14 * 5 cm
C ≈ 31.4 cm
Therefore, the circumference of the circle is approximately 31.4 cm.
Question 3: Solve for the missing angle in a triangle
In a triangle, the sum of all angles is always 180 degrees. To solve for a missing angle, you can subtract the known angles from 180 degrees. In this question, two angles are given as 45 degrees and 60 degrees. Subtracting these angles from 180 degrees, we get:
180 degrees - 45 degrees - 60 degrees
75 degrees
Therefore, the missing angle in the triangle is 75 degrees.
Question 4: Determine the volume of a rectangular prism
To find the volume of a rectangular prism, you can use the formula V = length * width * height. In this question, the length is 8 cm, the width is 4 cm, and the height is 6 cm. Plugging in these values into the formula, we get:
V = 8 cm * 4 cm * 6 cm
V = 192 cm³
Therefore, the volume of the rectangular prism is 192 cm³.
Question 5: Calculate the surface area of a cylinder
The surface area of a cylinder can be found using the formula SA = 2πrh + 2πr², where π is a mathematical constant approximately equal to 3.14, r is the radius of the base, and h is the height of the cylinder. In this question, the radius is given as 3 cm and the height is given as 8 cm. Plugging in these values into the formula, we get:
SA = 2π * 3 cm * 8 cm + 2π * (3 cm)²
SA ≈ 2 * 3.14 * 3 cm * 8 cm + 2 * 3.14 * (3 cm)²
SA ≈ 150.72 cm² + 56.52 cm²
SA ≈ 207.24 cm²
Therefore, the surface area of the cylinder is approximately 207.24 cm².
Question 6: Find the perimeter of a rectangle
The perimeter of a rectangle can be found by adding up the lengths of all its sides. In this question, the length is given as 12 cm and the width is given as 5 cm. Adding up the lengths of all sides, we get:
Perimeter = 2 * length + 2 * width
Perimeter = 2 * 12 cm + 2 * 5 cm
Perimeter = 24 cm + 10 cm
Perimeter = 34 cm
Therefore, the perimeter of the rectangle is 34 cm.
Question 7: Determine the area of a trapezoid
To find the area of a trapezoid, you can use the formula A = 1/2 * (b₁ + b₂) * h, where b₁ and b₂ are the lengths of the bases and h is the height. In this question, the lengths of the bases are given as 8 cm and 12 cm, and the height is given as 6 cm. Plugging in these values into the formula, we get:
A = 1/2 * (8 cm + 12 cm) * 6 cm
A = 1/2 * 20 cm * 6 cm
A = 60 cm²
Therefore, the area of the trapezoid is 60 cm².
Question 8: Solve for the missing side length of a right triangle
In a right triangle, you can use the Pythagorean theorem to solve for the missing side length. The theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this question, the lengths of the other two sides are given as 5 cm and 12 cm. Let's solve for the hypotenuse:
c² = a² + b²
c² = 5 cm² + 12 cm²
c² = 25 cm² + 144 cm²
c² = 169 cm²
c = √169 cm
c = 13 cm
Therefore, the missing side length of the right triangle is 13 cm.
Question 9: Calculate the surface area of a rectangular prism
The surface area of a rectangular prism can be found by adding up the areas of all its faces. In this question, the length is given as 6 cm, the width is given as 4 cm, and the height is given as 5 cm. Let's calculate the surface area:
Surface Area = 2lw + 2lh + 2wh
Surface Area = 2 * 6 cm * 4 cm + 2 * 6 cm * 5 cm + 2 * 4 cm * 5 cm
Surface Area = 48 cm² + 60 cm² + 40 cm²
Surface Area = 148 cm²
Therefore, the surface area of the rectangular prism is 148 cm².
Question 10: Find the volume of a cone
The volume of a cone can be found using the formula V = 1/3 * πr²h, where π is a mathematical constant approximately equal to 3.14, r is the radius of the base, and h is the height of the cone. In this question, the radius is given as 4 cm and the height is given as 10 cm. Plugging in these values into the formula, we get:
V = 1/3 * 3.14 * (4 cm)² * 10 cm
V ≈ 1/3 * 3.14 * 16 cm² * 10 cm
V ≈ 1/3 * 3.14 * 160 cm³
V ≈ 167.47 cm³
Therefore, the volume of the cone is approximately 167.47 cm³.
Question 11: Determine the area of a parallelogram
To find the area of a parallelogram, you can use the formula A = base * height, where the base is one of the sides of the parallelogram and the height is the perpendicular distance between the base and the opposite side. In this question, the base is given as 8 cm and the height is given as 5 cm. Plugging in these values into the formula, we get:
A = 8 cm * 5 cm
A = 40 cm²
Therefore, the area of the parallelogram is 40 cm².
Question 12: Solve for the missing side length of a quadrilateral
To solve for the missing side length of a quadrilateral, you can use the fact that opposite sides of a parallelogram are equal in length. In this question, three side lengths are given as 6 cm, 8 cm, and 10 cm. Let's solve for the missing side length:
Let x be the missing side length.
6 cm + 8 cm + 10 cm + x = 2 * (6 cm + 8 cm)
24