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

Question

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

Video Solution

Solution Steps

00:00 Find the area of the kite
00:03 First, let's find the area of the rectangle
00:08 Multiply side(30) by side(20)
00:12 This is the area of rectangle ABCD
00:22 Let's draw the diagonals in the kite and mark them with letters PMNK
00:31 Now let's use the formula to calculate the kite's area
00:35 (diagonal (PN) multiplied by diagonal (MK)) divided by 2
00:40 The diagonals are equal to the sides of the rectangle
00:43 Let's substitute appropriate values and solve to find the kite's area
00:50 And this is the solution to the problem

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

Answer

300 m

More Questions

Related Subjects

Area of a Deltoid (Kite) Calculating the Area of a Rectangle Area Kite Rectangle

Question Types

Area of a Rectangle: Using additional geometric shapes Area of a Deltoid: Using additional geometric shapes