Knowee
Questions
Features
Study Tools

Length of the fence of a trapezium shaped field ABCD is 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC

Question

Length of the fence of a trapezium shaped field ABCD is 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC

🧐 Not the exact question you are looking for?Go ask a question

Solution

To find the area of a trapezium, we use the formula:

Area = 1/2 * (sum of parallel sides) * height

Here, the parallel sides are AD and BC, and the height is AB. However, we don't know the lengths of AB and BD yet.

First, we need to find the length of BD. We know that the total perimeter of the trapezium is 120 m. So,

BD = Perimeter - (AD + BC + CD) BD = 120 - (40 + 48 + 17) BD = 120 - 105 BD = 15 m

Now, we can find the length of AB using the Pythagorean theorem, since triangle ABD is a right triangle.

AB = sqrt(AD^2 - BD^2) AB = sqrt(40^2 - 15^2) AB = sqrt(1600 - 225) AB = sqrt(1375) AB = 37.08 m (approx)

Now we can find the area of the trapezium:

Area = 1/2 * (AD + BC) * AB Area = 1/2 * (40 + 48) * 37.08 Area = 1/2 * 88 * 37.08 Area = 1631.52 square meters (approx)

So, the area of the trapezium shaped field is approximately 1631.52 square meters.

This problem has been solved

Similar Questions

A trapezium ABCD is inscribed in a circle of radius 17 cm. Sides AB and CD are parallel, and the perpendicular distance between them is 23 cm. If AB = 16 cm, then what is the area (in sq. cm) of the trapezium ABCD?

The area of a trapezium shaped field is 480 m2 , the distance between two parallel sides is 15 m and one of the parallel side is 20 m. Find the other parallel side.

ABCD is a trapezium in which AB||DC and P and Q arepoints on AD and BC respectively such that PQ||DC .If PD = 12 cm, BQ = 42 cm and QC = 18 cm, find AD.

A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field.Marks : 1Negative Marks : 0Answer here185169144196

Calculate the area of the triangle shown.View Image DescriptionA triangle labeled ABC on a coordinate plane.Side AC labeled 17 m.The height of the triangle is indicated by a dashed line that extends from angle B, through the interior of the triangle, to side AC. It is labeled 12 m.68 meters squared102 meters squared80 meters squared204 meters squared

1/3

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.