https://file.aiquickdraw.com/mathbot/file/17267327207220o61u8b5.jpg

Let's break down the problem step by step based on the image of the right pyramid \( ABCDV \):

### Given Information:
1. The base of the pyramid is a rectangle with:
   - \( AB = DC = 2x \) cm
   - \( AD = BC = x \) cm
2. The edges \( VA, VB, VC, VD \) are all of equal length.
3. The angle between \( VA \) and the base \( ABCD \) is \( 45^\circ \).
4. The volume of the pyramid is \( \frac{9}{5} \, \text{cm}^3 \

Figure 4 shows a right pyramid ABCDV. The base of the pyramid is a rectangle where AB = DC = 2x cm and AD = BC = x cm. The edges VA, VB, VC, and VD are all of equal length. The angle between VA and ABCD is 45 degrees. (a) Show that VA = (√10/2)x cm. (b) Find the exact height of the pyramid in terms of x. (c) Find the size of angle VBA. (d) Find the size of the obtuse angle between plane AVC and plane BVD. (e) Given that the volume of the pyramid is 9/5 cm³, find the value of x.

Solve a right pyramid geometry problem where the base is a rectangle, and the edges are equal. Learn how to apply Pythagoras' Theorem, trigonometric ratios, and volume formulas to find the height and dimensions of the pyramid.

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