Calculate Deltoid Area: Using 12cm and 16cm Diagonals

Deltoid Area with Perpendicular Diagonals

ABDC is a deltoid.

AB = BD

DC = CA

AD = 12 cm

CB = 16 cm

Calculate the area of the deltoid.

161616121212CCCAAABBBDDD

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Calculate the kite's area
00:03 Let's use the formula for calculating a kite's area
00:12 (diagonal multiplied by diagonal) divided by 2
00:18 Let's substitute appropriate values and solve to find the area
00:34 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

ABDC is a deltoid.

AB = BD

DC = CA

AD = 12 cm

CB = 16 cm

Calculate the area of the deltoid.

161616121212CCCAAABBBDDD

2

Step-by-step solution

First, let's recall the formula for the area of a rhombus:

(Diagonal 1 * Diagonal 2) divided by 2

Now we will substitute the known data into the formula, giving us the answer:

(12*16)/2
192/2=
96

3

Final Answer

96 cm²

Key Points to Remember

Essential concepts to master this topic
  • Rule: Deltoid area equals half the product of diagonal lengths
  • Technique: Area = d1×d22=12×162 \frac{d_1 \times d_2}{2} = \frac{12 \times 16}{2}
  • Check: Verify diagonals are perpendicular and calculation gives 96 cm² ✓

Common Mistakes

Avoid these frequent errors
  • Adding diagonals instead of multiplying
    Don't add diagonals like 12 + 16 = 28! This completely ignores the area concept and gives a linear measurement instead of area. Always multiply the diagonals first, then divide by 2 for the correct area formula.

Practice Quiz

Test your knowledge with interactive questions

Look at the deltoid in the figure:

555666

What is its area?

FAQ

Everything you need to know about this question

What makes a deltoid different from other quadrilaterals?

+

A deltoid (kite) has two pairs of adjacent equal sides: AB = BD and DC = CA. This creates perpendicular diagonals, which is key to using the diagonal area formula!

Why do we divide by 2 in the area formula?

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The diagonals split the deltoid into four triangles. The formula d1×d22 \frac{d_1 \times d_2}{2} calculates the total area of these triangles efficiently.

How do I know which measurements are the diagonals?

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Diagonals connect opposite vertices. In deltoid ABDC, the diagonals are AD (12 cm) and CB (16 cm) - they cross inside the shape at right angles.

Can I use this formula for any quadrilateral?

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No! This formula only works when diagonals are perpendicular (meet at 90°). It works for deltoids, rhombuses, and squares, but not rectangles or parallelograms.

What if I get the diagonals mixed up?

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It doesn't matter! Since you're multiplying the diagonals, the order doesn't change the result: 12 × 16 = 16 × 12 = 192, then ÷ 2 = 96 cm².

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