Question

What is the area of a triangle with vertices at (-4,1), (-7,5) and (0,1)

Answer 1

62.1467 square units (correct to four decimal places)

Explanation:

Let's say the triangle is;

A(-7,5)

B(-4,1)

C(0,1)

Let's say also that AB = a , BC = b and AC = c

By measurement BC = 4 units , AB = 5 units (applying Pythagorean theorem) and AC = 8.1 units (correct to one decimal place) also through Pythagorean theorem.

Area of this triangle =
`√(p(p-a)(p-b)(p-c))` , where p is half the perimeter of the triangle

p =
`(1)/(2)(4 + 8 + 8.1) = 8.55` units

Area =
`√(8.55(8.55-5)(8.55-4)(8.55-8.1))` = 62.1467 square units (correct to four decimal places)