Question

the parallel side of trapezium 12 cm and 17cm .its non parallel sides are equal each equal to 6.5cm considering the trapezium as the sum of a parallelogram and an isosceles triangle ,find its area​

Answer 1

Answer:

Area of trapezium = 87 cm²

Step-by-step explanation:

Given:

• The parallel side of a trapezium are 12 cm and 17 cm.
• Non parallel sides are equal to 6.5 cm each

To Find:

• Area of the trapezium

Solution:

First we have to find the area of the triangle.

By Heron's formula we know that area of a triangle is given by,

$\sf{Area\:of\:a\:triangle=\sqrt{s(s-a)(s-b)(s-c)} }$

where s is the semipreimeter and a , b, c are the sides of the triangle respectively.

s = (6.5 + 6.5 + (17-12)/2)

s = (6.5 + 6.5 + 5)/2

s = 18/2 = 9

Substituting the value,

$\sf{Area\:of\:the\:triangle=\sqrt{9(9-6.5)(9-6.5)(9-5)} }$

Area of the triangle = √(9 × 2.5 × 2.5 ×4)

Area of the triangle = √225

Area of the triangle = 15 cm²

Now we have to find the altitude/height of the triangle.

1/2 × b × h = Area of the triangle

1/2 × 5 × h = 15

h = 15 × 2/5

h = 6 cm

Hence height of the parallelogram is 6 cm.

Now we have to find the area of the parallelogram,

Area of the parallelogram = base × height

Substitute the data,

Area of parallelogram  = 12 × 6

Area of parallelogram = 72 cm²

Now,

Area of trapezium = Area of triangle + Area of parallelogram

Area of trapezium = 15 + 72

Area of trapezium = 87 cm²

Hence area of the trapezium is 87 cm²