Find the perimeter of the figure. Round all figures to the nearest hundredths place. Isosceles trapezoid 13 ft 4 ft 9 ft a. 26.47 ft b. 26.90 ft c. 30.94 ft d. 24.45 ft

Question

asked Oct 23, 2022 154k views

2 Answers

Ilya Evdokimov · Answer 1 · 2022-10-29T12:55:46+0000

Given:

Consider the below figure attached with this question.

To find:

The per perimeter of the isosceles trapezoid. Round all figures to the nearest hundredths place.

Solution:

Consider the isosceles trapezoid is ABCD.

Draw two perpendicular from C and D to AB as shown in second figure.

Now, CDEF is a rectangle,

$EF=CD=9\text{ ft}$

AB-EF=13-9

$AB-EF=4\text{ ft}$

It is an isosceles trapezoid, so
$\Delta ADE\cong \Delta BCF$ .

$AE=BF=(4)/(2)=2\text{ ft}$

Now,

AE^2+DE^2=AD^2 [Pythagoras theorem]

2^2+4^2=AD^2

4+16=AD^2

√(20)=AD

$AD=BC\approx 30.94$ [Isosceles trapezoid]

Find the perimeter of the figure.

Perimeter=AB+BC+CD+AD

Perimeter=13+4.47+9+4.47

$Perimeter=30.94\text{ ft}$

Therefore, the correct option is c.