Adam has a playhouse in his backyard that is shaped like a square prism with a squarepyramid for the roof. what is the volume of his playhouse if the house is 3 ft x 3 ft x 5 ft high and the roof is 3 ft x 3 ft x 2 ft high

51 cubic feet

Step-by-step explanation:

This is basically a rectangular prism + pyramid.

Volume of rectangular prism = length * width * height

Volume of square pyramid = 1/3 * area of base * height

The rectangular prism's dimensions are 3 x 3 x 5 ,  so volume = 3*3*5 = 45

The pyramid's base is a square with side 3, so area of base = 3 * 3 = 9

The height is 2, we find the volume using the formula stated above as:

1/3 * 9 * 2 = 6

Volume of Playhouse = volume of rectangular prism + volume of pyramid

Volume of Playhouse = 45 + 6 = 51 cubic feet

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b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.