Gr 9 MATH: Ch 9.4 Solving Problems

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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?

Use a compass to draw a circle with a given radius from a central point (D) Signup and view all the answers

How do you construct a regular polygon using a protractor?

Divide 360° by the number of sides (B) Signup and view all the answers

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

d = √(l^2 + w^2) (A) Signup and view all the answers

What is the formula for the area of a triangle?

A = 1/2 × base × height (B) Signup and view all the answers

What is the formula for the perimeter of a triangle?

P = a + b + c (D) Signup and view all the answers

What is the formula for the area of a square?

A = s^2 (A) Signup and view all the answers

What is the formula for the circumference of a circle?

C = 2πr (A) Signup and view all the answers

What is the formula for the area of a circle?

A = πr^2 (C) Signup and view all the answers

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

(n - 2) × 180° (D) Signup and view all the answers

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

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

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

a^2 + b^2 = c^2 (B) Signup and view all the answers

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

Compass (C) Signup and view all the answers

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

Drawing parallel opposite sides (A) Signup and view all the answers

What is the primary tool used in constructing a rhombus?

Compass (C) Signup and view all the answers

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

To find the angle between vertices (C) Signup and view all the answers

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

To draw the height (D) Signup and view all the answers

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

Use of a set square (B) 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?

40 square units (A), 40 square units (B) 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?

6 units (D) Signup and view all the answers

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

24 units (C) Signup and view all the answers

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

40 square units (D) Signup and view all the answers

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

153.94 square units (C) 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?

33.51 square units (B) Signup and view all the answers

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

720 degrees (A) Signup and view all the answers

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

159.11 square units (B) Signup and view all the answers

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

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

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

$P = 2(l + w)$ (D) Signup and view all the answers

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

$A = rac{ heta}{360} imes \pi r^2$ (A) Signup and view all the answers

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

To draw arcs from each endpoint of the base to intersect and form the other vertices (D) Signup and view all the answers

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

Using a set square to draw the height (A) Signup and view all the answers

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

$A = b imes h$ (A) Signup and view all the answers

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

$C = 2 \pi r$ (C) Signup and view all the answers

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

Dividing 360° by the number of sides (D) 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?

To measure the given angles (C) Signup and view all the answers

What is the primary tool used in constructing a circle?

Compass (D) Signup and view all the answers