Question

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Answer 1

Keys

• Isosceles triangle

Triangles having two equal sides.

• Pythagorean Theorem

If three lengths of a right triangle are $a$, $b$, and $c$, and the hypotenuse is $c$, $a^2+b^2=c^2$.

 

Solution

Let's draw a bisector of an angle. By triangle congruence, two triangles are congruent. (Attachment 1)

One isosceles triangle is two right triangles. (Attachment 2)

 

Applying Pythagorean Theorem,

Base: 12 cm

Height: 8 cm

 

Area of one triangle

$=\dfrac{1}{2} \times 12\times 8$

$=48$ cm²

 

Area of the rectangle

$=16\times 12$

$=192$ cm²

 

The figure is a sum of the areas of two triangles and one rectangle.

 

Area of the polygon

$=2\times 48+192$

$=96+192$

$=288$ cm²

Answer 2

Answer:

Keys

Isosceles triangle

Triangles having two equal sides.

Pythagorean Theorem

If three lengths of a right triangle are aa , bb , and cc , and the hypotenuse is cc , a^2+b^2=c^2a

2

+b

2

=c

2

.

 

Solution

Let's draw a bisector of an angle. By triangle congruence, two triangles are congruent. (Attachment 1)

One isosceles triangle is two right triangles. (Attachment 2)

 

Applying Pythagorean Theorem,

Base: 12 cm

Height: 8 cm

 

Area of one triangle

=\dfrac{1}{2} \times 12\times 8=

2

1

×12×8

=48=48 cm²

 

Area of the rectangle

=16\times 12=16×12

=192=192 cm²

 

The figure is a sum of the areas of two triangles and one rectangle.

 

Area of the polygon

=2\times 48+192=2×48+192

=96+192=96+192

=288=288 cm²