See diagram.

The area that can be grazed by the horse at each vertex is the area of the sector of radius 7 m at each vertex.

To find that area we need to know the angle at each vertex.

We use the cosine rule in a triangle as we know the lengths of the sides.

AC² = AB² + BC² - 2 AB * BC * Cos B

20² = 34² + 42² - 2 * 34 * 42 * Cos B

Cos B = 0.88235 => B = 28.07⁰

AB² = AC² + BC² - 2 AC * BC * Cos C

34² = 42² + 20² - 2 * 42 * 20 * Cos C

Cos C = 0.6 => C = 53.13°

A = 180° - B - C = 98.80°

Area grazed by the horse at the vertex A = (π * 7²) * (98.80°/360°) m²

= 42.247 m²

Area grazed by the horse at the vertex B = (π * 7² * (28.07°/360°) m²

= 12 m²

Area grazed by the horse at the vertex C = (π 7² * (53.13°/360°) m²

= 22.718 m²

Total area of the triangle ABC can be found by Heron's formula as:

s = semi perimeter = (AB+BC+CA)/2 = 48 m

The area left ungrazed is = 336 - 22.718 - 12 - 42.247 = 259.035 m²