Calculate Deltoid Area: Finding Area with Height 5 and Base 16

Question

Given the deltoid ABCD

Find the area

555161616AAADDDCCCBBB

Video Solution

Solution Steps

00:00 Find the area of the kite
00:03 We'll use the formula to calculate the kite's area
00:07 (diagonal times diagonal) divided by 2
00:13 We'll substitute the appropriate values according to the given data and solve for the area
00:26 We'll divide 16 by 2
00:37 And this is the solution to the question

Step-by-Step Solution

To find the area of the deltoid ABCD, we use the external height formula for deltoids:

Given:
- Height (hh) = 1616 cm
- Segment related to base (bb) = 55 cm

The area of the deltoid can be calculated by:

Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}

Plugging in our values, we have:

Area=12×5×16\text{Area} = \frac{1}{2} \times 5 \times 16

Calculating the result:

Area=12×80=40\text{Area} = \frac{1}{2} \times 80 = 40 cm2^2

Therefore, the area of deltoid ABCD is 4040 cm2^2.

Answer

40 40 cm².