Area and perimeter of triangles

Calculate the perimeter of the triangle.

The triangle is a scalene triangle with three sides of different lengths.

$$\text{Perimeter } = 7 + 8 + 9 = 24 \text{ cm}$$

Write the final answer.

$\text{Perimeter of the triangle} = 24 \text{ cm}$.

Convert the lengths to the same unit.

The diagram shows that $FE = 50 \text{ mm}$ and $DE = 17 \text{ cm}$. Before we can calculate the area of the triangle, we need to convert the lengths to the same unit.

$10 \text{ mm} = 1 \text{ cm}$, so we can divide $FE$ by $10$ to get a length in centimetres:

$$FE = 50 \text{ mm} = \frac{50}{10} = 5 \text{ cm}$$

Calculate the area of the triangle.

$$\begin{align} \text{Area of a triangle } &= \frac{1}{2} (b \times h) \\ \text{Area } \triangle DEF &= \frac{1}{2} (5 \times 17) \\ &= \text{42,5} \end{align}$$

Write the final answer.

$\text{Area } \triangle DEF = \text{42,5} \text{ cm}^2$.

Identify the perpendicular height of the triangle for base $YZ$.

We know the length of the side $YZ$ so we can take $YZ$ to be the base of the triangle. Vertex $X$ lies opposite the base $YZ$, so the correct perpendicular height for base $YZ$ is $XS$.

Note that $YT$ is the perpendicular height of the triangle for base $XZ$.

Calculate the area of the triangle.

$$\begin{align} \text{Area of a triangle } &= \frac{1}{2} (b \times h) \\ \text{Area } \triangle XYZ &= \frac{1}{2} (7 \times 6) \\ &= 21 \end{align}$$

Write the final answer.

$\text{Area } \triangle XYZ = 21 \text{ cm}^2$.