📐 geometry

1. **State the problem:** We need to find the volume of a solid composed of a right pyramid mounted on a rectangular block. Both have a square base of side length 6 cm. The block h

1. The problem is to find the area of a trapezoid with parallel sides measuring $1 \frac{1}{2}$ cm and $3 \frac{1}{2}$ cm, and a height of 4 cm. 2. Convert the mixed numbers to imp

1. **State the problem:** We have a floor with vertices at J(2,1), K(2,8), L(9,8), and M(9,1) on a coordinate plane. We need to identify the shape and find its perimeter and area.

1. **State the problem:** We have a solid made of a rectangular block with a square base 6 cm by 6 cm and height 10 cm, with a right pyramid on top having the same square base and

1. The problem states that a triangle is drawn with vertices A(5, 1), B(7, 6), and C(1, 3). 2. The graph shows point A plotted at (5, 5) instead of (5, 1).

1. **State the problem:** Find the perimeter and area of the polygon with vertices S(3,0), T(3,9), U(8,9), and V(8,0). 2. **Identify the shape:** The vertices form a rectangle beca

1. **State the problem:** Find the perimeter and area of the polygon with vertices J(1,2), K(7,2), L(7,8), and M(1,8). 2. **Identify the shape:** The polygon is a rectangle because

1. Problem 49: Find the ratio of the total surface area of three small cubes with side lengths 3 cm, 4 cm, and 5 cm to the surface area of a large cube made by combining their volu

1. **State the problem:** We have rectangle ABCD with perimeter 26.

1. **State the problem:** We have rectangle ABCD with perimeter 26. A half circle with diameter AD is inside the rectangle, and its area is given as $8\pi$. We need to find the per

1. The problem asks for the value of $x + y + z$ where $x$, $y$, and $z$ are central angles in a circle. 2. Recall that the sum of all central angles around a point in a circle is

1. **State the problem:** A man’s eyes are 1.75 m above sea level and he can barely see the top of a lighthouse 20 km away. We need to find the elevation of the lighthouse top abov

1. གྲུ་བཞི་དང་པང་གསུམ་གྱི་ཁ་ཕྱོགས་ཀྱི་འགྲུབ་འབྲས་ག་རེ་ཡིན་ཞིག་བསྐྱར་བཤད་གནང་བ་དགོས། 2. གྲུ་བཞི་དང་པང་གསུམ་གྱི་ཁ་ཕྱོགས་ནི་གྲུ་བཞི་གི་ཁ་ཕྱོགས་དང་པང་གསུམ་གྱི་ཁ་ཕྱོགས་ཡིན། དེ་ནི་གྲུ་བཞ

1. **State the problem:** We are given a rectangular prism with points A, B, C, D on the front face and E, F, G, H on the back face. We know the lengths CD = 2 cm, DE = 3 cm, and B

1. **State the problem:** We have two similar cylinders. The smaller cylinder has a volume of 800 cm^3 and a height of 10 cm. The larger cylinder has a height of 15 cm. We need to

1. **State the problem:** We are given a rectangular prism with points A, B, C, D, E, F, G, H and lengths CD = 65 cm, DE = 63 cm, and BD = 85 cm. We need to find the length of the

1. **State the problem:** We are given a circle with points D, C, A, and B. Point C lies on the vertical segment from D to A inside the circle. We need to find the angle $x^\circ$

1. **Problem statement:** Given a rectangular cuboid with points A, B, C, D on the front face and E, F, G, H on the back face, and given lengths CD = 20 cm, DE = 60 cm, and BD = 40

1. The problem is to plot the point $P(3, 4, -4)$ in a three-dimensional coordinate system. 2. The point $P$ has coordinates $x=3$, $y=4$, and $z=-4$.

1. The problem asks to identify which labelled angles on the triangular prisms are right angles. 2. A right angle measures exactly $90^\circ$.

1. نبدأ بتحديد طول السبلاج شاكي من الشكل المعطى، حيث طول السبلاج هو مجموع الأضلاع التي تحتوي على جذور. 2. الأضلاع المعطاة هي: