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olga_2 [115]
3 years ago
10

A right triangle is removed from a rectangle as shown in the figure. Find the area of the remaining part of the rectangle. [Area

of a triangle = 1/2(b)(h)]
Mathematics
1 answer:
IrinaVladis [17]3 years ago
8 0
I found the same problem with its corresponding image.

The rectangle has a length of 8 inches and width of 6 inches.
The right triangle was taken from the width. Its short leg measures 2 inches and the remainder of the width was 2 inches.

Area of the rectangle = Length x Width
A = 8 inches * 6 inches
A = 48 square inches.

Area of a right triangle = 1/2 a h
a is the short leg = 2 inches
h is the long leg = width - remainder of the width = 6 in. - 2 in. = 4 inches.

Area = 1/2 * 2 in. * 4in.
Area = (1*2*4)/2
A = 8/2
A = 4 square inches.

Area of Rectangle - Area of Triangle = Area of remaining figure.

48 sq. in - 4 sq. in. = 44 sq. inches.
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iren2701 [21]

Statement 1: WXYZ is a kite

Reason 1: Given

Statement 2: WX = XY and WZ = YZ

Reason 2: Definition of a kite

Statement 3: XZ = XZ

Reason 3: Reflexive property

Statement 4: Triangle WXZ = Triangle YXZ

Reason 4: SSS Congruence

Statement 5: Angle W = Angle Y

Reason 5: CPCTC

-------------------------------------------------------------------------

Extra notes:

* A kite is a quadrilateral that has two pairs of adjacent congruent sides. In this case, WX and XY is one pair of congruent sides that are adjacent (ie next to each other). So that's why WX = XY. Similarly, WZ = YZ is the second pair of adjacent congruent sides.

* Draw in a segment from point X to point Z to help form two triangles. The two triangles are congruent as proven in statement 4. One triangle is a reflection over the line XZ to get the other triangle.

* Due to this reflection, angle W reflects over line XZ to get angle Y. Proving that angle W = angle Y

* SSS means "side side side", basically saying "you use three pairs of congruent sides to prove two triangles congruent".

* The acronym CPCTC stands for "corresponding parts of congruent triangles are congruent"

4 0
3 years ago
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