Since one side is 40°, you subtract that from 180.
180° - 40°= 140°.
So therefore your missing side lengths are 140, 40, and 140.
hopefully this helps
*I am assuming that the hexagons in all questions are regular and the triangle in (24) is equilateral*
(21)
Area of a Regular Hexagon:
square units
(22)
Similar to (21)
Area =
square units
(23)
For this case, we will have to consider the relation between the side and inradius of the hexagon. Since, a hexagon is basically a combination of six equilateral triangles, the inradius of the hexagon is basically the altitude of one of the six equilateral triangles. The relation between altitude of an equilateral triangle and its side is given by:


Hence, area of the hexagon will be:
square units
(24)
Given is the inradius of an equilateral triangle.

Substituting the value of inradius and calculating the length of the side of the equilateral triangle:
Side = 16 units
Area of equilateral triangle =
square units
Answer:
b = 9
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
b² + 12² = 15²
b² + 144 = 225 ( subtract 144 from both sides )
b² = 81 ( take the square root of both sides )
b =
= 9
Answer: -31
<u>Step-by-step explanation:</u>
f(x) = -x⁴ + 3x³ + x² - 8x - 16
f(3) = -(3)⁴ + 3(3)³ + (3)² - 8(3) - 16
= -81 + 81 + 9 - 24 - 16
= -31