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Answer:
The Area of Shaded region is 98 square inch
Step-by-step explanation:
In this given figure
length = 8 in = 3 + x
breadth = 4 + y
In a Rectangle
a shape with four straight sides and four angles of 90 degrees (right angles). Two of the sides are longer than the other two
Now, let the smaller side be x and bigger side be y
Here, we get the equation
x + 3 = 8
x + 3 - 3 = 8 - 3
x = 5
Here, we get the value of x is 5
Now, By Pythagoras Theorem
x² + y² = 13²
(5)² + y² = 169 (x = 5)
25 + y² = 169
y² + 25 - 25 = 169 - 25
y² = 144
√y² = √144
y = 12
So, breadth = 4 + 12 = 16 inch
Now, For the area of rectangle
A = l × b
A = 8 × 16 in
A = 128 square inch
In a given triangle,
b = y = 12 in
h = x = 5 in
Now, For the area of Triangle
<em>A = ½ × b × </em><em>h</em>
A = ½ × 12 × 5 in
A = 6 × 5 in
A = 30 Square inch
So, For the shaded area,
= Area of Rectangle - Area of triangle
= 128 - 30
= 98 square inch
Thus, The Area of Shaded region is 98 square inch
<u>-</u><u>TheUnknownScientist</u>
The additional information needed to prove both triangles are similar are:
A. ∠B ≅ ∠M
C. △ABC was rotated and dilated by a scale factor between 0 and 1
E. ∠C ≅ ∠L
<h3>What are Similar Triangles?</h3>When a triangle is rotated and dilated by a scale factor, the new triangle formed has the same shape but different size of the original triangle. However, all its corresponding angles remains congruent.
Thus, for triangles ABC and NML to be similar to each other, since we already known each have one congruent right angles, the additional information needed are:
A. ∠B ≅ ∠M
C. △ABC was rotated and dilated by a scale factor between 0 and 1
E. ∠C ≅ ∠L
Learn more about similar triangles on:
#SPJ1
