Question

Work out the length of AM, then find the area of the triangle.
*PLEASE REFER TO IMAGE BELOW*

Answer 1

see explanation

Explanation:

ΔABC is isosceles and AM is the perpendicular bisector to BC, hence

BM = MC = 4 cm

Using Pythagoras' identity on ΔABM, then

AB² = AM² + BM², that is

7² = AM² + 4²

49 = AM² + 16 ( subtract 16 from both sides )

33 = AM² ( take the square root of both sides )

AM =
`\sqrt33}`

The area (A) of ΔABC is found using

A =
`(1)/(2)` bh ( b is the base BC and h the height AM )

A =
`(1)/(2)` × 8 ×
`√(33)` = 4
`√(33)` cm² ≈ 23 cm²