Question

Find the area of the triangle belowBe sure to include the correct unit in your answer.15 cm20 cm25 cm

Answer 1

To find the area of the triangle given the dimensions as 15cm, 20cm and 25cm

Recall that the area of a traingle is given as

$\begin{gathered} \text{Area = }\frac{1}{2}\times base\times height \\ \text{where the base of the triangle in the question is 15cm and the height is 20cm} \\ \text{Area = }\frac{1}{2}\times15\operatorname{cm}\times20\operatorname{cm} \\ \text{Area = 15cm }\times\text{ 10cm} \\ =150cm^2 \end{gathered}$

Alternatively, we can use the Hero's formula

$\begin{gathered} \text{Area = }\sqrt{s(s\text{ -a )(s-b)(s-c)}} \\ \text{where s = }\frac{a+b+c}{2} \\ \text{Thus, s = }\frac{15\text{ + 20 + 25}}{2}\text{ = }\frac{60}{2}\text{ = 30} \\ \text{Area = }\sqrt{30(30-15)(30-20)(30-25)} \\ \text{Area = }\sqrt{30(15)(10)(5)} \\ \text{Area = }\sqrt{22500} \\ \text{Area = 150cm}^2 \end{gathered}$