Question

determine whether each statement about the solid is true or false. statement 1: it is a pyramid. select choice statement 2: it has 5 faces. select choice statement 3: the base is a pentagon. select choice statement 4: it has 11 edges. select choice statement 5: it is a hexagonal pyramid. select choice

Explanation:

Step1: Recall pyramid definition

A pyramid has a polygon - base and triangular faces that meet at a single vertex. The given solid has a polygon base \(ABCDE\) and triangular faces meeting at \(F\), so it is a pyramid.

Step2: Count the faces

The base \(ABCDE\) is 1 face and there are 4 triangular faces (\(\triangle ABF\), \(\triangle BCF\), \(\triangle CDF\), \(\triangle ADF\)), so there are \(1 + 4=5\) faces.

Step3: Identify the base shape

The base has 5 vertices \(A\), \(B\), \(C\), \(D\), \(E\), so the base is a pentagon.

Step4: Count the edges

The base has 5 edges (\(AB\), \(BC\), \(CD\), \(DE\), \(EA\)) and there are 5 edges connecting the vertices of the base to the apex \(F\) (\(AF\), \(BF\), \(CF\), \(DF\), \(EF\)), so there are \(5 + 5 = 10\) edges, not 11.

Step5: Recall hexagonal - pyramid definition

A hexagonal - pyramid has a hexagon (6 - sided polygon) as a base. Since the base here is a pentagon, it is not a hexagonal pyramid.

Answer:

Statement 1: True
Statement 2: True
Statement 3: True
Statement 4: False
Statement 5: False