Calculate the Area of a Deltoid: 8x11 Unit Dimensions Problem

Question

Given the deltoid ABCD

Find the area

888111111AAADDDCCCBBB

Video Solution

Solution Steps

00:03 Let's find the area of the kite.
00:07 We will use a simple formula to calculate its area.
00:12 Multiply the length of one diagonal by the other. Then, divide by 2.
00:17 Next, substitute the given values into the formula and solve for the area.
00:31 First, divide 8 by 2.
00:40 And that's how we find the solution to this problem!

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the given information.
  • Step 2: Use the appropriate formula for area calculation.
  • Step 3: Perform the calculation using the formula.

Now, let's work through each step:
Step 1: We recognize that the vertical diagonal AC=8AC = 8 cm and the horizontal diagonal BD=11BD = 11 cm.
Step 2: We'll use the formula for the area of a deltoid (kite), given by
A=12×d1×d2A = \frac{1}{2} \times d_1 \times d_2, where d1d_1 and d2d_2 are the lengths of the diagonals.
Step 3: Plugging in our values, we get:
A=12×8×11A = \frac{1}{2} \times 8 \times 11
A=12×88A = \frac{1}{2} \times 88
A=44A = 44 cm².

Thus, the area of the deltoid is 44 44 cm².

Answer

44 44 cm².