# There are two triangles. One has a base of 8 cm and a height of 10 cm. The other has a base of 5 cm and a height of 13 cm. Which triangle has a larger area?

May 6, 2016

The triangle with base 8 cm and height 10 cm.

#### Explanation:

$A r e a \triangle = \frac{1}{2} \cdot b a s e \cdot h e i g h t$

${\triangle}_{1} a r e a = \frac{1}{2} \cdot 8 \cdot 10$
$= 40$

${\triangle}_{2} a r e a = \frac{1}{2} \cdot 5 \cdot 13$
$= 32.5$

$40 > 32.5 \therefore$ Area of first triangle is larger.

May 6, 2016

base 8 , height 10

#### Explanation:

The area (A) of a triangle is found as follows.

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{A = \frac{1}{2} b h} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

where b , is the base and h , the perpendicular height

For b = 8 and h = 10 :$A = \frac{1}{2} \times 8 \times 10 = 40 \text{ square cm}$

For b = 5 and h = 13 :$A = \frac{1}{2} \times 5 \times 13 = 32.5 \text{ square cm}$

Hence the triangle with b = 8 and h = 10 has the larger area.