Gr 9 MATH: Ch 9.4 Solving Problems
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Questions and Answers

What is the formula to find the perimeter of a polygon?

  • P = √(l^2 + w^2)
  • P = Sum of all side lengths (correct)
  • P = 2(l + w)
  • P = l + w

    • What is the method used to construct a triangle given two sides and an included angle?

  • AAA
  • SAS (correct)
  • ASA
  • SSS

    • How do you construct a parallelogram?

  • Use a compass to draw four equal sides
  • Draw the base and use a set square to draw the height, and then draw the opposite sides (correct)
  • Draw the base and use a protractor to measure the given angles
  • Use a ruler to draw four equal sides and ensure all angles are 90°

    • What is the method used to construct a circle?

    <p>Use a compass to draw a circle with a given radius from a central point</p> Signup and view all the answers

    How do you construct a regular polygon using a protractor?

    <p>Divide 360° by the number of sides</p> Signup and view all the answers

    What is the formula to find the diagonal of a rectangle?

    <p>d = √(l^2 + w^2)</p> Signup and view all the answers

    What is the formula for the area of a triangle?

    <p>A = 1/2 × base × height</p> Signup and view all the answers

    What is the formula for the perimeter of a triangle?

    <p>P = a + b + c</p> Signup and view all the answers

    What is the formula for the area of a square?

    <p>A = s^2</p> Signup and view all the answers

    What is the formula for the circumference of a circle?

    <p>C = 2πr</p> Signup and view all the answers

    What is the formula for the area of a circle?

    <p>A = πr^2</p> Signup and view all the answers

    What is the formula for the sum of the interior angles of a regular polygon?

    <p>(n - 2) × 180°</p> Signup and view all the answers

    What is the formula for the area of a regular polygon?

    <p>A = 1/4 × n × s^2 × cot(π/n)</p> Signup and view all the answers

    What is the formula for the Pythagorean theorem for a right triangle?

    <p>a^2 + b^2 = c^2</p> Signup and view all the answers

    What is the primary tool used in constructing a triangle given three sides?

    <p>Compass</p> Signup and view all the answers

    In constructing a quadrilateral, what ensures opposite angles are equal in a parallelogram?

    <p>Drawing parallel opposite sides</p> Signup and view all the answers

    What is the primary tool used in constructing a rhombus?

    <p>Compass</p> Signup and view all the answers

    In constructing a regular polygon, what is the purpose of dividing 360° by the number of sides?

    <p>To find the angle between vertices</p> Signup and view all the answers

    What is the purpose of using a set square in constructing a parallelogram?

    <p>To draw the height</p> Signup and view all the answers

    In constructing a quadrilateral, what ensures all angles are 90° in a rectangle?

    <p>Use of a set square</p> Signup and view all the answers

    What is the area of a Triangle with a base of 8 units and a height of 10 units?

    <p>40 square units</p> Signup and view all the answers

    A triangle has sides of length 3, 4, and 5 units. What is the semi-perimeter of this triangle?

    <p>6 units</p> Signup and view all the answers

    What is the perimeter of a square with a side length of 6 units?

    <p>24 units</p> Signup and view all the answers

    A rectangle has a length of 8 units and a width of 5 units. What is its area?

    <p>40 square units</p> Signup and view all the answers

    What is the area of a circle with a radius of 7 units?

    <p>153.94 square units</p> Signup and view all the answers

    A sector has a central angle of 60 degrees and a radius of 8 units. What is its area?

    <p>33.51 square units</p> Signup and view all the answers

    What is the sum of the interior angles of a regular hexagon?

    <p>720 degrees</p> Signup and view all the answers

    What is the area of a regular octagon with a side length of 5 units?

    <p>159.11 square units</p> Signup and view all the answers

    What is the formula to find the area of a triangle using Heron's formula?

    <p>$A = \sqrt{s(s - a)(s - b)(s - c)}$</p> Signup and view all the answers

    What is the formula to find the perimeter of a rectangle?

    <p>$P = 2(l + w)$</p> Signup and view all the answers

    What is the formula to find the area of a sector of a circle?

    <p>$A = rac{ heta}{360} imes \pi r^2$</p> Signup and view all the answers

    What is the purpose of using a compass in constructing a triangle given three sides?

    <p>To draw arcs from each endpoint of the base to intersect and form the other vertices</p> Signup and view all the answers

    What is the key to ensuring all angles are 90° in a rectangle during construction?

    <p>Using a set square to draw the height</p> Signup and view all the answers

    What is the formula to find the area of a parallelogram?

    <p>$A = b imes h$</p> Signup and view all the answers

    What is the formula to find the circumference of a circle?

    <p>$C = 2 \pi r$</p> Signup and view all the answers

    What is the key to constructing a regular polygon using a protractor?

    <p>Dividing 360° by the number of sides</p> Signup and view all the answers

    What is the purpose of using a protractor in constructing a triangle given two angles and an included side?

    <p>To measure the given angles</p> Signup and view all the answers

    What is the primary tool used in constructing a circle?

    <p>Compass</p> Signup and view all the answers

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