Calculate the Area of a Deltoid with Diagonals 7 and 10 Units

Question

Given the deltoid ABCD

Find the area

101010777CCCBBBAAADDD

Video Solution

Solution Steps

00:03 Let's find the area of the kite.
00:06 We're going to use a special formula for the area of a kite.
00:11 It's diagonal one times diagonal two, all divided by 2.
00:16 Now, let's plug in the given values and solve to find the area.
00:31 We need to divide 10 by 2.
00:40 And that's the solution to our question!

Step-by-Step Solution

To solve this problem, we need to calculate the area of the deltoid using the formula for the area in terms of diagonals:

  • Identify the two diagonals: AC=10AC = 10 cm and BD=7BD = 7 cm.
  • Use the formula for the area of a deltoid: A=12×d1×d2 A = \frac{1}{2} \times d_1 \times d_2 .
  • Substitute the values of the diagonals into the formula: A=12×10×7=702=35 A = \frac{1}{2} \times 10 \times 7 = \frac{70}{2} = 35 .

Thus, the area of the deltoid is 35 cm2\textbf{35 cm}^2.

Therefore, the solution to the problem is 35 cm2\textbf{35 cm}^2, which corresponds to choice 3.

Answer

35 35 cm².