In an isosceles trapezoid the length of a diagonal is 25 cm and the length of an altitude is 15 cm. Find the area of the trapezoid. Lots of points

Question

asked Jan 10, 2019 164k views

2 Answers

Amir Sasson · Answer 1 · 2019-01-16T06:11:54+0000

Answer:

The area of the trapezoid is
$525\ cm^(2)$

Explanation:

we know that

The area of a isosceles trapezoid is equal to the area of two isosceles right triangles plus the area of a rectangle

step 1

Find the area of the isosceles right triangle

Remember that

In a isosceles right triangle the height is equal to the base of the triangle

we have

$h=15\ cm$

so

$b=15\ cm$

The area is equal to

A=(1)/(2)(b)(h)

substitute the values

$A=(1)/(2)(15)(15)=112.5\ cm^(2)$

step 2

Find the area of the rectangle

The area of the rectangle is equal to

A=LW

we have

$W=15\ cm$ -----> is the height of the trapezoid

$d=25\ cm$ -----> the diagonal of the rectangle

Applying the Pythagoras Theorem

$25^(2)=L^(2)+15^(2)\\L^(2)=25^(2)-15^(2) \\ L^(2) =400\\L=20\ cm$

The area of the rectangle is

$A=(20)(15)=300\ cm^(2)$

step 3

Find the area of the trapezoid

$A=2(112.5\ cm^(2))+300\ cm^(2)=525\ cm^(2)$