Rectangle Diagonal Problem: Calculate Triangle Area with BO = 8.5 and AD = 8

Question

Below is the rectangle ABCD.

O is the intersection point of the diagonals of the rectangle.

AD = 8

BO = 8.5

Calculate the area of the triangle ABD.

00:00 Calculate the area of triangle ABD

00:03 Lengths according to the given data

00:07 In a rectangle, the diagonals bisect each other

00:15 Now let's use the Pythagorean theorem in triangle ABD

00:19 Let's substitute appropriate values and solve for AB

00:31 Let's isolate AB

00:37 This is the length of side AB

00:40 Now let's use the formula for calculating triangle area

00:43 (base(15) times height(8)) divided by 2

00:47 And this is the solution to the question

According to the given information, we can claim that:

$BD=2BO=8.5\times2=17$

Now let's look at triangle ABD to calculate side AB

$AB^2+AD^2=BD^2$

Let's input the known data:

$AB^2+8^2=17^2$

$AB^2=289-64=225$

We'll take the square root

$AB=15$

Now let's calculate the area of triangle ABD:

$\frac{15\times8}{2}=\frac{120}{2}=60$