Question

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​

Answer 1

Hey Ashamnasha !

Answer:

196 m²

Step-by-step explanation:

Given :

AB = 10 m

BC = 14 m

CD = 25 m

DA = 13 m

To Find :

Area of a Trapezium shaped field with the given measurements.

Formulae :

Area of a triangle = ½bh units²

• Where b is the base of the triangle,
• h is the corresponding height.

Area of a triangle = √[(s)(s - a)(s - b)(s - c)] units²

• Where a,b,c are the sides of the triangle and
• s is the semi-perimeter of the triangle. i.e. s = ½(a + b + c)

Area of a Trapezium = ½h(a + b) units²

• Where h is the altitude between the parallel sides and
• a and b are the measures of the parallel sides.

Procedure :

We draw two lines from A and B respectively, both perpendicular to CD. Let the intersection points be X and Y respectively. (Refer the attached picture)

[Also QR = 15 Because QR = DX + YC, which is DC - AB = 25 m - 10 m = 15 m.]

Now Area of the Triangle PQR = √[(s)(s - a)(s - b)(s - c)]

Where :

• a = 13 m
• b = 14 m
• c = 15 m
• s = ½(13 m + 14 m + 15 m) = 21 m

=> Area(∆PQR) = √[(21 m)(21 m - 13 m)(21 m - 14 m)(21 m - 15 m)]

=> Area(∆PQR) = √[(21 m)(8 m)(7 m)(6 m)]

=> Area(∆PQR) = √[7 × 3 × 2³ × 7 × 2 × 3 m⁴]

=> Area(∆PQR) = √[7² × 3² × 2⁴] m²

=> Area(∆PQR) = 7 × 3 × 2² m²

Hence Area(∆PQR) = 84 m².

Area(∆PQR) is also = (½ × QR × h) m²

=> 84 = ½ × 15 × h

=> h = (168/15) m

Now we know h, we can find Area of Trapezium as a and b are also given.

=> Area(ABCD) = ½ × (168/15 m) × (10 m + 25 m)

=> Area(ABCD) = [(84/15) × 35] m²

=> Area(ABCD) = [(84/3) × 7] m²

=> Area(ABCD) = (28 × 7) m²

Hence Area of Trapezium field ABCD = 196 m².

Hope this helps you !

Thanks !