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

The area of the trapezoid is

Step-by-step 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

so

The area is equal to

substitute the values

step 2

Find the area of the rectangle

The area of the rectangle is equal to

we have

-----> is the height of the trapezoid

 -----> the diagonal of the rectangle

Applying the Pythagoras Theorem

The area of the rectangle is

step 3

Find the area of the trapezoid

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

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step-by-step explanation: