Calculate the Area of a Deltoid Stage: 30m × 20m Field Problem

A deltoid-shaped stage is to be built in a rectangular field.

The length of the field is 30 m and the width is 20 m.

Determine the area of the stage shaded in orange?

202020303030AAABBBCCCDDD

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:08 Let's determine how to find the area of the kite.
00:12 First step, let's find the area of the rectangle.
00:16 We multiply the side of thirty by the side of twenty.
00:20 This gives us the area of rectangle A B C D.
00:30 Next, we draw the diagonals of the kite and label them as P M N K.
00:39 Now, let's use the formula to calculate the kite's area.
00:43 It's diagonal P N times diagonal M K, all divided by two.
00:49 Remember, the diagonals are equal to the sides of the rectangle.
00:53 Substitute in these values, and then solve to find the kite's area.
00:58 Great job! That's how we solve the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

A deltoid-shaped stage is to be built in a rectangular field.

The length of the field is 30 m and the width is 20 m.

Determine the area of the stage shaded in orange?

202020303030AAABBBCCCDDD

2

Step-by-step solution

We can calculate the area of rectangle ABCD as follows:

20×30=600 20\times30=600

Now let's divide the deltoid along its length and width and add the following points:

202020303030PPPMMMNNNKKKAAABBBCCCDDDFinally, we can calculate the area of deltoid PMNK as follows:

PMNK=PN×MK2=20×302=6002=300 PMNK=\frac{PN\times MK}{2}=\frac{20\times30}{2}=\frac{600}{2}=300

3

Final Answer

300 m

Practice Quiz

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Indicate the correct answer

The next quadrilateral is:

AAABBBCCCDDD

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