Question

A trapezoid field has parallel sided measuring 70 m and 20 m. A horse is tetheredat each
corner of the field with a rope of length 3.5 m. Find the area not grazed by the horses if
the perpendicular distance between the parallel sides is 28 m.

Answer 1

Answer:

The Area that is not grazed by the horse is 1221.5 sq meters .

Step-by-step explanation:

Given as :

A horse is tethered to each corner of trapezoid field with rope of length 3.5 m

The parallel side measure = 70 m  ,  20 m

The none parallel sides = 28 m

Let The Area that is not grazed by the horse = A sq m

According to question

The Area of Trapezoidal field = $\dfrac{1}{2}$ × ( sum of parallel side ) × height

Or,  Area of Trapezoidal field = $\dfrac{1}{2}$ × ( 70 m + 20 m ) × 28 m

∴   Area of Trapezoidal field = $\dfrac{1}{2}$ × ( 90 m ) × 28 m

or,  Area of Trapezoidal field = $\dfrac{1}{2}$ × 2520 m²

or, Area of Trapezoidal field = 1260 sq m

Again

Area that grazed by horse at each corner = 4 × area of semi-circle

or, Area that grazed by horse at each corner = 4 × $\dfrac{1}{4}$ × π × radius²

or, Area that grazed by horse at each corner = 3.14 × (3.5 m)²

∴ Area that grazed by horse at each corner = 38.46 sq m

Now,

Area that is not grazed by the horse =  Area of Trapezoidal field - Area that grazed by horse at each corner

Or, A = 1260 sq m - 38.46 sq m

∴ A = 1221.5 sq m

Or, Area = 1221.5 sq m

Hence, The Area that is not grazed by the horse is 1221.5 sq meters . Answer