Question

the area of triangle formed by points (0,8) , (0,0) , (8,0).​

Answer 1

Answer:

32 sq. units

Step-by-step explanation:

Given the coordinates of vertices of a triangle.

• (0,8)
• (0,0)
• (8,0)

Now, to find the area of the triangle.

We know that,

Area of a triangle having coordinate of vertices as (a,b) (c,d) and (e,f) is given by,

Area = ½ × | a(d-f) - b(c-e) + 1(cf - de)|

Here, we have,

• (a,b) = (0,8)
• (c,d) = (0,0)
• (e,f) = (8,0)

Therefore, we will get,

=> A = ½ × |0(0-0) - 8(0-8) +1(0 - 0)|

=> A = ½ × | 0(0) - 8(-8) + 1(0)|

=> A = ½ × |0 + 64 + 0|

=> A = ½ × |64|

=> A = ½ × 64

=> A = 32

Hence, area of triangle is 32 sq. units.

Answer 2

Given: A triangle formed by the points (0, 8), (0, 0) and (8, 0).

To find: The area.

Answer:

Formula to find the area of a triangle:

$\tt Area\ =\ \dfrac{1}{2}\ \times\ \Bigg(x_1\Big(y_2\ -\ y_3\Big)\ +\ x_2\Big(y_3\ -\ y_1\Big)\ +\ x_3\Big(y_1\ +\ y_2\Big)\Bigg)$

From the given points, we have:

$\tt x_1\ =\ 0\\\\x_2\ =\ 0\\\\x_3\ =\ 8\\\\y_1\ =\ 8\\\\y_2\ =\ 0\\\\y_3\ =\ 0$

Using them in the formula,

$\tt Area\ =\ \dfrac{1}{2}\ \times\ \Bigg(0\Big(0\ -\ 0\Big)\ +\ 0\Big(0\ -\ 8\Big)\ +\ 8\Big(8\ -\ 0\Big)\Bigg)\\\\\\Area\ =\ \dfrac{1}{2}\ \times\ \Bigg(0\ +\ 0\ +\ 64\Bigg)\\\\\\Area\ =\ \dfrac{1}{2}\ \times\ 64\\\\\\\bf Area\ =\ 32\ units^2$

Therefore, the area of a triangle formed by the points (0, 8), (0, 0) and (8, 0) is 32 units².