Compute the area <em>A</em> of ∆ABC.

• Take AB to be the base and CX (which is an altitude of ∆ABC) to be the height. Then the area is

<em>A</em> = 1/2 • AB • CX = 1/2 • 75 • CX

• Now take AC to be the base and BY (also an altitude) to be the height. Then

<em>A</em> = 1/2 • AC • BY = 1/2 • 70 • 60 = 2100

The areas must be equal, so we have

2100 = 1/2 • 75 • CX → CX = 4200/75 = **56**

**Answer:**

The area of the shaded = 8 - 2π units²

**Step-by-step explanation:**

The area of the shaded portion = area square - area not shaded portion

Not shaded portion consists of two equal segments

∵ The side of the square = the radius of the circle = **2**

∵ The measure of each angle of the square = **π/2** (90° = π/2 rad)

∵ Area each segment = Area sector - area triangle

∵ Area triangle = 1/2 × (2) × (2) = **2** units²

∵ Area sector = (1/2)r²Ф ⇒ r = 2 , Ф = π/2

∴ Area sector = (1/2) (2)² (π/2) = **π** units²

∴ Area each segment = **π - 2**

∴ Area not shaded = 2(π - 2) = **2π - 4** units² ⇒ two segment

∵ Area square = 2 × 2 = **4** units²

∴ Area shaded portion = 4 - (2π - 4) = 4 - 2π + 4

= **8 - 2π** units²

A integer that is divisible by 2 can be -2,-4,-6,4,2,6 or something else, but these are simpler.

**Answer:**

**Step-by-step explanation:**

The area of the pentagonal base, A = 33.5 cm²

The height of the prsim,h = 15 cm

We need to find the volume of the pentagonal base prism. The formula for the volume of the pentagonal base prism is given by :

So, the required volume is .