Imagine and solve

Geometry Level pending

A solid, whose bases are right triangle at the top and rectangle at the bottom, has one of its edges perpendicular to bases and connecting the vertex of right angle of the triangle and one of the vertices of rectangle. Two of its edges are lines that connect the vertices of the triangle away from the right angle to a vertex of the rectangle diagonally opposite to the vertex where perpendicular line connects. Another two lines connects the vertices of the smaller angles of triangles to remaining vertices of the rectangle nearest to it. If the legs of the right triangle are 8 and 6; the leg of length 8 is opposite to a side of rectangle of length 10 and leg of length 6 opposite to side of length 8, and the height of the solid is 15, what would be the volume of the solid?

The answer is 830.

1 solution

Jade Mijares
May 10, 2016

What I am describing is this

(Yet not scaled properly)

Finding the area of triangular base (letting it be $b$ )

$b = \frac{(8)(6)}{2}$ $b = 24$

Then for rectangular base (letting it be $B$ )

$B = (10)(8)$ $B = 80$

Using the sides of the bases, and finding means, the resulting figure will be:

finding its area (denoted by $M$ )

$M = (5)(7) + \frac{(7+4)(4)}{2}$ $M = 57$

Using the formula for volume of prismatoid,

$V = \frac{[b+B+4(M)](15)}{6}$ $V = \frac{[24+80+4(57)](15)}{6}$ $\boxed{V = 830}$

Imagine and solve

The answer is 830.

1 solution

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