Calculate the Diagonal Length in a Deltoid: Given Area 32 cm² and AC = 8 cm

Shown below is the deltoid ABCD.

The diagonal AC is 8 cm long.

The area of the deltoid is 32 cm².

Calculate the diagonal DB.

S=32S=32S=32888AAABBBCCCDDD

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Calculate diagonal DB
00:03 We'll use the formula for calculating the area of a kite
00:06 (diagonal times diagonal) divided by 2
00:10 We'll substitute appropriate values and solve for BD
00:17 Multiply by 2 to eliminate the fraction
00:26 Isolate BD
00:30 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Shown below is the deltoid ABCD.

The diagonal AC is 8 cm long.

The area of the deltoid is 32 cm².

Calculate the diagonal DB.

S=32S=32S=32888AAABBBCCCDDD

2

Step-by-step solution

First, we recall the formula for the area of a kite: multiply the lengths of the diagonals by each other and divide the product by 2.

We substitute the known data into the formula:

8DB2=32 \frac{8\cdot DB}{2}=32

We reduce the 8 and the 2:

4DB=32 4DB=32

Divide by 4

DB=8 DB=8

3

Final Answer

8 cm

Practice Quiz

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Indicate the correct answer

The next quadrilateral is:

AAABBBCCCDDD

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