Question

question 1.16
suppose you want to determine the approximate area of a lake at a recreational park using the information given in the parks brochure. the triangles on the map apply to locations of picnic areas. the distances between the sites are given on the map.
use geometric shapes to model the area of the lake. use your model to estimate the area of the lake.
the lake has an approximate area of square yards

Explanation:

Step1: Divide the lake into two triangles

We can consider the lake as composed of two non - overlapping triangles. Let's assume the bridge divides the lake into two triangles.

Step2: Use Heron's formula for triangle area (if needed) or simple triangle area formula

For a triangle with base $b$ and height $h$, the area of a triangle $A=\frac{1}{2}bh$. Let's assume one triangle has base $b_1 = 572$ yards and height $h_1=244$ yards, and the other has base $b_2 = 800$ yards and height $h_2 = 244$ yards.
The area of the first triangle $A_1=\frac{1}{2}\times572\times244$
$A_1 = 572\times122=69784$ square yards.
The area of the second triangle $A_2=\frac{1}{2}\times800\times244$
$A_2=400\times244 = 97600$ square yards.

Step3: Calculate the total area of the lake

The total area of the lake $A = A_1+A_2$
$A=69784 + 97600=167384$ square yards.

Answer:

167384