Define the term triangle.

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11. Define the term triangle.
A triangle is a polygon with three straight sides and three vertices. It is a closed two-dimensional shape whose interior angles sum to $180^\circ$ .

12. Classify the following triangles with angles:

a) $60^\circ, 60^\circ, 60^\circ$ : Equilateral triangle (all angles are equal, implying all sides are equal).

b) $70^\circ, 40^\circ, 70^\circ$ : Isosceles triangle (two angles are equal, implying two sides are equal).

c) $40^\circ, 72^\circ, 68^\circ$ : Scalene triangle (all angles are different, implying all sides are different).

13. Calculate both the perimeter and area for the following:

a)

Calculate the perimeter.
The sides of the triangle are $9 \text{ cm}$ , $12 \text{ cm}$ , and $15 \text{ cm}$ .
$\text{Perimeter} = 9 \text{ cm} + 12 \text{ cm} + 15 \text{ cm}$ $\text{Perimeter} = \boxed{\text{}36 \text{ cm}\text{}}$
Calculate the area.
The base is $15 \text{ cm}$ and the height is $6 \text{ cm}$ .
$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ $\text{Area} = \frac{1}{2} \times 15 \text{ cm} \times 6 \text{ cm}$ $\text{Area} = \frac{1}{2} \times 90 \text{ cm}^2$ $\text{Area} = \boxed{\text{}45 \text{ cm}^2\text{}}$
b)
Calculate the area.
The base is $7 \text{ cm}$ and the height is $4 \text{ cm}$ .
$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ $\text{Area} = \frac{1}{2} \times 7 \text{ cm} \times 4 \text{ cm}$ $\text{Area} = \frac{1}{2} \times 28 \text{ cm}^2$ $\text{Area} = \boxed{\text{}14 \text{ cm}^2\text{}}$
Note: The perimeter cannot be calculated without the length of the third side. The given side $2.5 \text{ cm}$ is one of the non-base sides.

c)
The given side lengths are $3 \text{ cm}$ , $3 \text{ cm}$ , and $8 \text{ cm}$ .
According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Here, $3 \text{ cm} + 3 \text{ cm} = 6 \text{ cm}$ .
Since $6 \text{ cm} < 8 \text{ cm}$ , a triangle cannot be formed with these dimensions.

14. In the triangle below, angles at A and B are $55^\circ$ and $115^\circ$ respectively. Find the value of $x$ at C.
Find the interior angle at B.
The exterior angle at B is $115^\circ$ . The interior angle at B and the exterior angle at B are supplementary (they add up to $180^\circ$ ).
$\text{Interior Angle at B} = 180^\circ - 115^\circ$ $\text{Interior Angle at B} = 65^\circ$
Use the sum of angles in a triangle.
The sum of the interior angles of a triangle is $180^\circ$ .
$\text{Angle A} + \text{Interior Angle B} + \text{Angle C} = 180^\circ$ $55^\circ + 65^\circ + x = 180^\circ$ $120^\circ + x = 180^\circ$
Solve for $x$ .
$x = 180^\circ - 120^\circ$ $x = \boxed{\text{}60^\circ\text{}}$

Define the term triangle.

Step-by-step solution

Calculate the perimeter.

Calculate the area.

Calculate the area.

Find the interior angle at B.

Use the sum of angles in a triangle.

Solve for $x$ .

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More Mathematics Questions

Define the term triangle.

Step-by-step solution

Calculate the perimeter.

Calculate the area.

Calculate the area.

Find the interior angle at B.

Use the sum of angles in a triangle.

Solve for xxx.

Still stuck on this one?

More Mathematics Questions

Solve for $x$ .