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Exam 6: Geometry

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Question 51

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A building near the docks in Hamburg, Germany has a cross-section in the shape of a parallelogram with base $86.0 \mathrm{~m}$ and height $20.9 \mathrm{~m}$ . What is the area of the cross-section?

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Question 52

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Determine the height of an equilateral triangle with a side $5.1 \mathrm{in}$ .

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Question 53

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Determine the value of angles $A$ and $B$ .

What is the length of a diagonal of a square whose side is $12.5 \mathrm{~cm}$ ?

A coping stone is in the form of a right prism with a cross-section in the shape of an equilateral triangle. The length of the prism is $10 \mathrm{~cm}$ and its volume is $27 \mathrm{~cm}^{3}$ . Determine the length of the triangular edges.

Determine the length of $B C$ if the diameter of the circle is $60.0 \mathrm{~cm}$ .

Find the volume of a right circular cone with base diameter $12.0 \mathrm{~m}$ and slant height is $10.0 \mathrm{~m}$ .

The area of a regular hexagon (six equal sides and six equal angles) is $190.5 \mathrm{~cm}^{2}$ . Determine the length of its side.

Determine the area of this figure:

A kite frame is made in the shape of a rhombus where one of the angles is $135^{\circ}$ . It is covered by 2912 $\mathrm{cm}^{2}$ of fabric. What is the side length of the kite?

The perimeter of an equilateral triangle is $17.6 \mathrm{~mm}$ . What is its area?

What is the circumference of a circular pond having an area of $22.9 \mathrm{~m}^{2}$ ?

The area of an equilateral triangle is $15.5 \mathrm{~cm}^{2}$ . What is its side length?

Determine the height of a tree if its shadow is $20.3 \mathrm{~m}$ long at same time that a one metre stick has a shadow $1.4 \mathrm{~m}$ long.

One brand of solar collector can generate $12 \mathrm{~W} / \mathrm{m}^{2}$ . If one such collector is triangular in shape with base $3.75 \mathrm{~m}$ and altitude $5.55 \mathrm{~m}$ , how many watts of power can it generate?

A parallelogram with a side length of 9.1 inches is inscribed inside a circle of diameter 14 inches, as shown. Determine the area of the shaded region.

Determine the value of angle $\theta$ .

Determine the volume of a right circular cylinder that has a lateral surface area equal to $440 \mathrm{~cm}^{2}$ and a height of $55 \mathrm{~cm}$ .

The outside diameter of an empty spherical container is $18.0 \mathrm{~cm}$ and the thickness of its wall is 3.00 $\mathrm{cm}$ . Determine the volume of the wall material of the container.

Determine the length of $A B$ if the diameter of the circle is $60.0 \mathrm{~cm}$ .