Calculating the Area of a Deltoid with Height 5 and Base 6
Kite Area with Diagonal Measurements
Look at the deltoid in the figure:
What is its area?
❤️ Continue Your Math Journey!
We have hundreds of course questions with personalized recommendations + Account 100% premium
Step-by-step video solution
Step-by-step written solution
Understand the problem
Look at the deltoid in the figure:
What is its area?
Step-by-step solution
To solve the exercise, we first need to know the formula for calculating the area of a kite:
It's also important to know that a concave kite, like the one in the question, has one of its diagonals outside the shape, but it's still its diagonal.
Let's now substitute the data from the question into the formula:
(6*5)/2=
30/2=
15
Final Answer
15
Key Points to Remember
- Formula: Kite area equals product of diagonals divided by 2
- Technique: Use
- Check: Verify diagonals are perpendicular and formula gives reasonable result ✓
Common Mistakes
- Confusing kite with triangle area formula Don't use base × height ÷ 2 for kites = wrong answer like 15 instead of using diagonal formula! Kites need the diagonal product formula because their diagonals are perpendicular bisectors. Always use diagonal₁ × diagonal₂ ÷ 2 for kites.
Practice Quiz
Indicate the correct answer
The next quadrilateral is:
FAQ
What makes this shape a kite and not a rhombus?
+A kite has two pairs of adjacent sides that are equal, while a rhombus has all four sides equal. This deltoid (concave kite) has its vertex pointing inward, creating the distinctive kite shape.
Why do we use diagonal measurements instead of side lengths?
+Kite area formulas use diagonals because they're always perpendicular in kites! This makes the diagonal formula much simpler than trying to calculate with irregular side lengths.
How can I tell which measurements are the diagonals?
+Diagonals connect opposite vertices and cross each other at right angles. In the figure, the height (5) and base (6) lines represent the two diagonals of this kite.
Does it matter that this is a concave kite?
+No! Whether the kite is convex or concave (like this deltoid), the area formula stays the same. The diagonal formula works for both types of kites.
What if I calculated 30 instead of 15?
+You probably forgot to divide by 2! The formula is , not just . Always remember that final division step.
🌟 Unlock Your Math Potential
Get unlimited access to all 18 Deltoid questions, detailed video solutions, and personalized progress tracking.
Unlimited Video Solutions
Step-by-step explanations for every problem
Progress Analytics
Track your mastery across all topics
Ad-Free Learning
Focus on math without distractions
No credit card required • Cancel anytime