Basic Geometry
1.
Find the perimeter of a rectangle 19 cm long by 27.8 cm wide.
2.
In triangle ABC, angle A = 47°, and angle B = 8°. Find angle C.
3.
Find the perimeter of a triangle with sides of length 28 cm, 47 cm and 19 cm.
4.
In triangle FGH, angle F = 32°, and angle G = 100°. Find angle H.
5.
Find the circumference of a circle whose radius is 27 in.
(use 3.14 for π).
6.
Find the area of the trapezoid.
7.
Find the area of a triangular piece of cloth that has a 18 cm base and is 24 cm high.
8.
Find the area of a circle with a radius of 39 cm (use 3.14 for π).
9.
Find the area of a rectangle 17 m by 13 m.
10.
Find the area of the triangle with a base of 27 ft and height of 24 ft:
11.
Find the volume of the box:
12.
Find the volume of a sphere with a 15 in. radius.
13.
Find the volume of a cone that is 18 in. high and has a 6 in. radius.
14.
Find the volume of a cylinder that is 15 in. high and has a 10 in. radius.
15.
Find the volume of a box that is 12 feet long, 27 feet high and 3 feet wide.
Do you expect us to do your homework for you? Think again.
Surely you have seen formulas such as these. Use them.
2. C = 180 - A - B degrees
5. Circumference = 2*pi*R
10. Area = (1/2)*Base*Height
12. Volume = (4/3)*pi*R^3
16. Volume = Width*Length*Depth
1. To find the perimeter of a rectangle, you simply need to add up all the sides. In this case, the rectangle is 19 cm long and 27.8 cm wide. So, the perimeter would be 2 times the length plus 2 times the width.
Perimeter = 2(19 cm) + 2(27.8 cm)
Perimeter = 38 cm + 55.6 cm
Perimeter = 93.6 cm
Therefore, the perimeter of the rectangle is 93.6 cm.
2. In a triangle, the sum of the angles is always 180°. Given that angle A is 47° and angle B is 8°, you can find angle C by subtracting the sum of angles A and B from 180°.
Angle C = 180° - (Angle A + Angle B)
Angle C = 180° - (47° + 8°)
Angle C = 180° - 55°
Angle C = 125°
Therefore, angle C is 125°.
3. To find the perimeter of a triangle, you need to add up the lengths of all three sides. In this case, the triangle has sides of length 28 cm, 47 cm, and 19 cm.
Perimeter = 28 cm + 47 cm + 19 cm
Perimeter = 94 cm
Therefore, the perimeter of the triangle is 94 cm.
4. Similar to question 2, in a triangle, the sum of the angles is always 180°. Given that angle F is 32° and angle G is 100°, you can find angle H by subtracting the sum of angles F and G from 180°.
Angle H = 180° - (Angle F + Angle G)
Angle H = 180° - (32° + 100°)
Angle H = 180° - 132°
Angle H = 48°
Therefore, angle H is 48°.
5. The circumference of a circle can be found using the formula C = 2πr, where C represents the circumference, π represents the mathematical constant pi (approximately 3.14), and r represents the radius of the circle. In this case, the radius of the circle is given as 27 in.
Circumference = 2π(27 in)
Circumference = 2(3.14)(27 in)
Circumference = 169.56 in
Therefore, the circumference of the circle is approximately 169.56 in.
(Note: The value of π is usually given as 3.14 in basic geometry, but for more precise calculations, you can use a more accurate approximation like 3.14159.)
6. To find the area of a trapezoid, you can use the formula A = (a + b) × h / 2, where A represents the area, a and b represent the lengths of the parallel sides, and h represents the height of the trapezoid. However, the trapezoid's measurements are not provided, so the area cannot be determined.
7. To find the area of a triangle, you can use the formula A = (base × height) / 2. In this case, the base is given as 18 cm and the height is given as 24 cm.
Area = (18 cm × 24 cm) / 2
Area = 216 cm²
Therefore, the area of the triangular piece of cloth is 216 cm².
8. The area of a circle can be found using the formula A = πr², where A represents the area, π represents the mathematical constant pi (approximately 3.14), and r represents the radius of the circle. In this case, the radius of the circle is given as 39 cm.
Area = 3.14 × (39 cm)²
Area = 3.14 × 1521 cm²
Area = 4782.54 cm²
Therefore, the area of the circle is approximately 4782.54 cm².
9. To find the area of a rectangle, you simply need to multiply the length by the width. In this case, the rectangle is 17 m by 13 m.
Area = 17 m × 13 m
Area = 221 m²
Therefore, the area of the rectangle is 221 m².
10. The area of a triangle can be found using the formula A = (base × height) / 2. In this case, the base is given as 27 ft and the height is given as 24 ft.
Area = (27 ft × 24 ft) / 2
Area = 324 ft²
Therefore, the area of the triangle is 324 ft².
11. To find the volume of a box, you need to multiply the length, width, and height. However, the measurements of the box are not provided, so the volume cannot be determined.
12. The volume of a sphere can be found using the formula V = (4/3)πr³, where V represents the volume, π represents the mathematical constant pi (approximately 3.14), and r represents the radius of the sphere. In this case, the radius is given as 15 in.
Volume = (4/3) × 3.14 × (15 in)³
Volume = 4.186 × 3.14 × 3375 in³
Volume = 44,265.75 in³
Therefore, the volume of the sphere is approximately 44,265.75 in³.
13. The volume of a cone can be found using the formula V = (1/3)πr²h, where V represents the volume, π represents the mathematical constant pi (approximately 3.14), r represents the radius of the cone's base, and h represents the height of the cone. In this case, the height is given as 18 in and the radius is given as 6 in.
Volume = (1/3) × 3.14 × (6 in)² × 18 in
Volume = 3.14 × 36 in² × 18 in/3
Volume = 3.14 × 36 in² × 6 in
Volume = 6780.48 in³
Therefore, the volume of the cone is approximately 6780.48 in³.
14. The volume of a cylinder can be found using the formula V = πr²h, where V represents the volume, π represents the mathematical constant pi (approximately 3.14), r represents the radius of the cylinder's base, and h represents the height of the cylinder. In this case, the height is given as 15 in and the radius is given as 10 in.
Volume = 3.14 × (10 in)² × 15 in
Volume = 3.14 × 100 in² × 15 in
Volume = 4710 in³
Therefore, the volume of the cylinder is 4710 in³.
15. To find the volume of a box, you need to multiply the length, width, and height. In this case, the box is 12 feet long, 27 feet high, and 3 feet wide.
Volume = 12 ft × 27 ft × 3 ft
Volume = 972 ft³
Therefore, the volume of the box is 972 ft³.