Deltoid Problem: Solve for 'a' Given Area 6a and Diagonals 2a+2 and a

Given the deltoid ABCD

The main diagonal is equal to 2a+2

Secondary diagonal is equal to a

The area of the deltoid equals 6a

Calculate a a

Video Solution

Solution Steps

00:00 Find A

00:03 Use the formula for calculating the area of a kite

00:07 Product of diagonals divided by 2

00:17 Substitute appropriate values according to the given data, and solve for A

00:37 Multiply by 2 to eliminate the fraction

00:41 Open parentheses properly, multiply by each factor

00:50 Arrange the equation so that one side equals 0

01:06 Factor out common terms from the parentheses

01:12 Find the possible solutions

01:15 A must be positive since it represents a physical length of a side

01:20 And this is the solution to the problem

Step-by-Step Solution

To solve the question, we first need to remember the formula for the area of a kite:

Diagonal * Diagonal / 2

This means that if we substitute the given data we can see that:

a(2a+2)/2 = area of the kite

Let's remember that we are also given the area, so we'll put that in the equation too

a(2a+2)/2 = 6a

Now we have an equation that we can easily solve.

First, let's get rid of the fraction, so we'll multiply both sides of the equation by 2

a(2a+2)=6a*2
a(2a+2)=12a

Let's expand the parentheses on the left side of the equation

2a²+2a=12a

2a²=10a

Let's divide both sides of the equation by a

2a=10

Let's divide again by 2

a=5

And that's the solution!