### Area of Isosceles Right Triangle

The area of an isosceles right triangle (derived from 0.5bh) is equal to the square of its base divided by 4, where b is the base and h is the height of the isosceles right triangle.

Recall that base angles of an isosceles triangle are equal. Since an isosceles right triangle is a right-angled isosceles triangle, the base angles of an isosceles right triangle are equal.

Question 1:
Where is the base of an isosceles right triangle?

The side between the base angles is the base.

Question 2:
Where is the height of an isosceles right triangle?

The height is a straight line drawn from the right angle to bisect the base.

An isosceles right triangle has two 45° angles and one 90° angle. The two 45° angles are the base angles and the 90° angle is the right angle. The base is the straight line between the two 45° angles and the height is the straight line drawn from the right angle to the mid-point between the two 45° angles.

Consider an isosceles right triangle ABC, where A and B are the base angles and C is the right angle. The three sides of the triangle are AB, BC and AC. The height is a vertical line drawn from C to the mid-point of AB, which means that the height and the base of an isosceles right triangle are two perpendicular lines.

Let the mid-point of the base be M. Then, the height is equal to CM.

In an isosceles right triangle, CM = AM = MB. Hence, the height is equal to half It's base.

h = b/2

Recall that the general formula of the area A of a triangle is 0.5bh.

Substituting 0.5b for h,
A (Area) = 0.5b × 0.5b
= 0.25 (b × b)

Example:
The base of an isosceles right triangle is 4cm. What is the area of the isosceles right triangle?

Solution:
b (base)     = 4cm
h (height) = 0.5b
= 0.5 × 4cm
= 2cm

Area (A) = 0.5bh
= 0.5 × 4cm × 2cm
= 4cm (squared)

Alternatively,
A = 0.25 (b × b)

b = 4cm

Substituting 4 for b,
A = 0.25 (4cm × 4cm)
= 0.25 × 16cm (squared)
= 4cm (squared)

### Qibla Compass

Qibla compass is a compass design showing clearly that Islam is a direction, and Muslims constitute just one out of the many directions of a compass. Some of the other directions of the compass are Sikhism, Gnosticism, Judaism, Hinduism, Christianity, Atheism, Psychology, Philosophy, Jainism, Zoroastrianism, Buddhism, Taoism, Baha'i Faith, Babism, Rastafarianism, etc.

Qibla compass is designed specifically to help Muslims locate the direction of Mecca and pray facing the Kaaba. Some designs have the word "Mecca" inscribed as the most prominent direction on the compass; others have the image of the Kaaba or a Mosque signifying the qibla (Muslim direction) on the compass.
Although Judaism doesn't have a compass to show Jews what direction to face during prayers, the fact that Jews all over the world pray toward the Temple Mount is an evidence that Judaism is a direction and the Temple Mount is the qibla of the Jews.
Every religion is a compass - the centre of the comp…

### Gaokerena

In Zoroastrianism, the World Tree (the tree of life described in Revelation 22) is called the mighty Gaokerena.
The mighty Gaokerena was a mythic Haoma plant that had healing properties when eaten and gave immortality to the resurrected bodies of the dead. (Wikipedia)
Wondering how large is the mighty Gaokerena? The tree is visible during binary black hole merger in gravitational wave astronomy. Consider the size of a black hole and how many black holes are there; that is the size of the giant Gaokerena.

The healing property of the Gaokerena is the reconciliation demonstrated whenever two black holes are merged to form a single black hole during binary black hole merger.

Islam and Christianity are two examples of two conflicting religions. The apostle Paul described the Christians as the Children of the day, which means that the Christians constitute the sun.
For you are all childrenof light, children of the day. We are not of the night or of the darkness. (1 Thessalonians 5:5) "E…

### Mandala

Mandala is a two dimensional representation of the axis mundi: the junction between the physical and the metaphysical. The physical is man or the earth, the metaphysical is God or heaven (sky), and Mandala is where God and man or heaven (sky) and earth are reconciled.

The universe is the sum of heaven and earth.

Universe = Heaven (Sky) + Earth

A mandala (emphasis on first syllable; Sanskrit मण्डल, maṇḍala – literally "circle") is a spiritual and ritual symbol in Hinduism and Buddhism, representing the universe(Wikipedia)
We learnt from the Taiji that the axis mundi represents balance or stability. Therefore the universe of the axis mundi is the orderly universe known as the cosmos, which means that Mandala is a two-dimensional representation of the cosmos.

"mandala" has become a generic term for any diagram, chart or geometric pattern that represents the cosmos metaphysically or symbolically; a microcosm of the universe. (Wikipedia)
Mandala is simply a square and …

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