Area of an Isosceles Triangle – Formulas and Examples

We can use the following values:

• Height, $latex h=7$ m
• Base, $latex b=6$ m

Therefore, using the formula with these values, we have:

$latex A= \frac{1}{2} \times b  \times h$

$latex A= \frac{1}{2} (6)(7)$

$latex A=21$

The area of the triangle is 21 m².

We have the information:

• Height, $latex h=11$ m
• Base, $latex b=10$ m

Substituting these values in the area formula, we have:

$latex A= \frac{1}{2} \times b  \times h$

$latex A= \frac{1}{2} (10)(11)$

$latex A=55$

The area of the triangle is 55 m².

We have the following information:

• Height, $latex h=13$ m
• Base, $latex b=15$ m

Using this information in the formula, we have:

$latex A= \frac{1}{2} \times b  \times h$

$latex A= \frac{1}{2} (15)(13)$

$latex A=97.5$

The area of the triangle is 97.5 m².

We have the following lengths:

• Base, $latex b=8$ m
• Congruent sides, $latex a=10$ m

Therefore, we can use the second formula to find the area using the lengths of the sides instead of the height:

$latex h=\frac{1}{2}(\sqrt{{{a}^2}-\frac{{{b}^2}}{4}}\times b)$

$latex h=\frac{1}{2}(\sqrt{{{10}^2}-\frac{{{8}^2}}{4}}\times 8)$

$latex h=\frac{1}{2}(\sqrt{100-\frac{64}{4}}\times 8)$

$latex h=\frac{1}{2}(\sqrt{100-16}\times 8)$

$latex h=\frac{1}{2}(\sqrt{84}\times 8)$

$latex h=\frac{1}{2}(9.17\times 8)$

$latex h=\frac{1}{2}(73.36)$

$latex h=36.68$

The area of the triangle is 36.68 m².

We have the following information:

• Base, $latex b=12$ cm
• Congruent sides, $latex a=14$ cm

Therefore, we use these values in the second formula:

$latex h=\frac{1}{2}(\sqrt{{{a}^2}-\frac{{{b}^2}}{4}}\times b)$

$latex h=\frac{1}{2}(\sqrt{{{14}^2}-\frac{{{12}^2}}{4}}\times 12)$

$latex h=\frac{1}{2}(\sqrt{196-\frac{144}{4}}\times 12)$

$latex h=\frac{1}{2}(\sqrt{196-36}\times 12)$

$latex h=\frac{1}{2}(\sqrt{160}\times 12)$

$latex h=\frac{1}{2}(12.65 \times 12)$

$latex h=\frac{1}{2}(151.8)$

$latex h=75.9$

The area of the triangle is 75.9 cm².