Question

The trapezoid ABCD has bases AB = 15 and CD = 5, thigh AD = 9 and diagonal BD = 12. Find:

a) the height h

b) S

c) the perimeter P of the trapezoid

Please someone help me

Answer 1

The height of the trapezoid is 6.63 units

The perimeter of the trapezoid is 38 units

Explanation:

Whenever a geometry problem is given, it is often useful if it is sketched out. A sketch of this problem can be found in the image attached.

A)

We can see that a right-angled triangle is formed between points BED, with line BE being the height, h.

To get the dimensions of the line EB, we subtract the dimensions of DC from AB. This will give 15 -5 = 10

hence the dimensions of the righ angled triangle are

DE= h

DB = 12 (diagonal)

EB = 10

From Pythagoras' theorem,

`h =√(12^2 -10^2)=6.63`

The height of the trapezoid is 6.63

B)

We can get the perimeter of the trapezoid by adding the dimensions of all four sides together.

This will be

AD + DC + CB + AB

However we can assume for this case that it is a symmetrical trapezoid, and hence AD = CB

Thus, perimeter =

2 (AD) + DC +AB

2(9) +5 +15 = 38.

The perimeter of the trapezoid is 38 units